A stupidly thorough thesis on the conceptual origins of Amy Rose.

Oh boy, I could probs write a whole dissertation on this alone, but you are absolutely right.
When they set out to create "the Minnie to Sonic's Mickey", it very much wasnt just in regards to design. Amy and Sonic share a lot of similarities even in regards to personality and interests, (with some more obvious differences and discrepancies of course).

Fair enough. Still fun to think about regardless if you ask me.

This is where I strongly disagree, and I could present you with a mountain of examples that show that these elements of believing in fate and destiny extend beyond just the CD encounter and only continued to be made a sticking point all the way to even Sonic Forces. And, maybe I will later. Unfortunately, I'm on my way to work at the moment so my hands are tied.
All i can leave you with is Amy's faith continues to be a consistent elements of her personality in near every game she appears in, and when it isn't its usually missing due to a western writer not "getting it" resulting in its omission, or the translation not getting it, resulting in its ommision.
Off the top of my head, the original Japanese script for Heroes actually has Amy use idioms to the tune of "Me and Sonic are tied by the red thread of Fate". She has a strong fascination and association with things like wishes and shooting stars, etc.
While she hasn't visibly pulled out the tarot deck as frequently as she probably could (and in my opinion should), this is still very much a present and consistent part of her characterization over the course of the series.

 

Really, I think the fact her Hammer was called a Magical Hammer by itself suggests enough about it, but to elaborate on this one point, the reason it isn't the same is because of how it is done and perceived in universe.
In the case of them simply taking out objects, it's always treated as them pulling something out of a or putting something into a nonexistent pocket. This is something all the characters do and is treated as a normal thing in universe. Amy's hammer on the other hand is the only object where the fact she "brings it out of nowhere" and "no one knows where she puts it" is ever made special mention of, as if to say it is a curiosity. If it were simply like how characters pull chaos emeralds out of their pockets, there would be no reason for such a thing or to highlight it.

Would Storming Hearts and Tornado Hammer not be concrete enough examples then? She summons whirlwinds of hearts to attack. Not sure how I would really explain it otherwise.



She also has a very similar move in Sonic Battle, which states she shoots the tornadoes by thinking of Sonic when before she swings.

In fact, the Japanese script specifically refers to them as "アイのタツマキ" (Love Tornados).

"エミーのグランドショット。
ソニックを想いながらハンマーを振ることで、
アイのタツマキ が発生して、
相手にダメージを与える。

"Amy's Ground Shot. By swinging her hammer while thinking of Sonic, Tornado of Love is released and damages the opponent."

Speaking of Sonic Battle, anyone remember when Amy did this?

Speaking of instances that are different than other character simply pulling things out of their pockets, this one is a good example as Amy does....what she does in the above as opposed to just pulling it out from her non-existent pocket like Sonic does.




Then of course there is the dowsing.

While it's been stated Amy has dowsing in her repertoire and her ability to sense Sonic and find him with her "girlish intuition" is well known, she has shown that it isn't exclusive to Sonic.
This clip in particular is her idle quote in Rail Canyon from Sonic Heroes.
Dowsing itself is conceptually something that is tied to magic or the idea of superstition in general, and is usually tied to the idea of "the forces of the cosmos" if you will which also conceptually ties in with things like Tarot, In essence a pseudoscience.
Do note the use of the word "may" implying uncertainty. This suggests her method isn't normal general "sensing things" like say a DragonBall character does with Ki.
Downsing is often done via dowsing rods, sometimes even called Witching Rods, though Amy doesn't seem to use any such thing, it's not really a rule that one needs any tool to do it.

 

I think I presented a more than adequate case for why I think it is rather premature to dismiss it as mere hammer space. It wouldn't need to be addressed as a special case specifically for Amy if it was, since hammerspace is something all the characters have. Yet Amy's Hammer is the only time its resting place being a mystery is made a point of. Why?

Likewise I think it is dismissive here as then it is to uniquely dismiss anything Amy does and only her.
Her hearts are very visibly interacting in the world as opposed to things like characters eyes bulging out in a cartoon manner.
If its just a mere visual effect, I'd like to know the contextual purpose of it outside of the assertion that it is merely so.

I don't mean to sound hostile, but I think you are being overly dismissive. Whatever one wants to call what Amy is doing here, there is more than sufficient evidence that she has some kind of ability. How one wants to describe it or call it is honestly up to the individual. But to sweep all this corroborated evidence under the rug? Can't help but feel its very much just kind of plugging one's ears and putting on blinders.
I mean, it doesn't get much more overt than the game litterally called the hammer a Magical Hammer, and I can't help but feel the desire to deny any of this is out of a personal desire to frame the character a certain way in rejection to suggestions to the contrary.
Like, I don't know how one explains "Tornado Hammer" as anything but some kind of power. It's really not something you can dismiss whatsoever, and let alone given it isn't something that is a one off as it has for all intents and purposes appeared in 3 different games/instances.

Not sure what the Rose Typhoon is meant to be a "visual effect" of, but I do know it hurts people.

At the end of the day, the last post I made is simply a straightforward observation one makes just by looking at what's in front of them, as opposed to merely whether they line up with preconceptions of what I believed the character was. With that, I do very much leave it up to the rest of everyone else to make sense of it how they please, but I must be transparent in saying I find it rather frustrating that some would rather, quite frankly, patronize by insisting "there is no war in Ba Sing Se" for a lack of a better way to describe it.

With that said, I don't see why this idea would conflate with one's perception of the character in the first place. Amy's growth over the course of the series isn't diminished or less prevalent any of this in mind. Rather, it reinforces the idea that her hard work paid off and yielded potent results.
If you perceives Amy as having an affinity for the mystical arts as something that has developed over the course of the series, which her Hammer being called a Magical Hammer in its debut game suggests, then it's still all just a series of tricks she picked up along the way acting as demonstrable proof of her evolution as an individual. I...just don't see how this conflates with anything in this regard to what you have expressed liking about the character.

Speaking of her Hammer. It's also been shown to change shape and size dynamically in multiple instances.
For good measure, i believe Sonic Adventure even states that it isn't a particularly powerful weapon, suggesting its efficiency is less physical. Which, well, makes sense given its modeled after a toy squeaky hammer of all things. Food for thought I suppose.

 

To start, I would like to point out how the only real "multiplayer" thing I listed as overt corroboration was Storming Hearts , so the "most" descriptor thing there is simply inaccurate.
(Rose Typhoon I believe supports my point, but if you want to ignore it, (which I don't agree with) be my guest. it's not a hill I want to die on.)
That said, I can't agree. Metal Sonic for example actually has no abilities. If they wanted the character to have none, nothing was stopping them from doing just that if they felt it. Even so, if we are to still take that out of the equation, it still reflects how the developers see the character and their abilities, and the things they do will at least have some form of descriptor to reflect the character. They could have done a lot of things instead of Storiming Hearts as an attack, such as cartoonishly having a hammer fall out of the sky and hit the player or have random objects flung at them cartoonishly like a move Amy had in Sonic the Fighters actually.
But they instead chose to specifically give her the ability to attack people with a whirlwind of hearts. That's not really random.
That I'd argue says something on its own, but could still be dismissed if not corroborated by the fact she has shown to be able to do similar if not conceptually identical moves in later entries even outside of Multiplayer such as the Tornado Hammer, and Pink Typhoon. It's in general, a concept they seem to see as something that extends beyond just a wacky excuse to hit the player in a single multiplayer mode in 1 game, unlike something like Knuckles' "Thunder Arrow" which as far as I am aware we never really see anything like it again.

Doesn't that HELP my case if anything? Amy actually has a lot of differences gameplay-wise. She is slower, doesn't have a spindash, light speed, dash, etc. They put thought into distinguishing her from the others, even going as far as having her whip out her hammer for every spin attack, somersault, homing attack she does to contextualise how she is doing it.
If it were just Sonic's Sonic Wind but Pink, I'd agree with you, but it has a completely different animation and uses different graphics. I see no good reason to dismiss this. They put extra thought and effort here that wasn't necessary if it was meant to be throwaway.

I mean, it's not even the first time she did it? If I remember correctly, it's actually something she could do in Sonic Drift, which, yes it's a game gear racing game. But nonetheless, its shows that this has a precedent and isn't "crazy". We see it on screen with our own eyes. In multiple instances.

I'm not sure how this contests the fact Amy has done Tornado Hammer. Blue Tornado and Black Tornado are basically clones of each other, but neither operates anything conceptually like Tornado Hammer of Espio's Leaf Swirl, which, I would hope we all agree is something he can categorically do as well as turn invisible along with it. So why is Amy being singled out here?
Like I said before, I am not making a categorical declaration on whatever it is Amy is doing. However one wants to describe what Amy does here is really up to the individual. I'm just saying that whatever that may be, she very clearly has "some" kind of power and this is simply my explanation of it, as I believe it to make sense in tying all the other things she has been shown to do together in a logical and neat manner that, at least to me, conceptually makes sense with her character.

Black knight.

 

So I was just minding my own business when I ran into something pretty cool.
As mentioned before, Amy has a move in called Pinky Typhoon where she summons Pink tornadoes she sends at her opponents.
Well as it turns out, Pinky Typhoon is the name of one of Sailor Chibi Moon's image themes from a Sailor Moon Musical.
This one supposedly came out January 2, 2003, same year as Sonic Battle released in Japan which was 4 December 2003 at the end of the year.
Can't really see how one shakes the connection on this one.