It's up to you on what to do since it is your project, but I personally think you should do whatever you feel will make it a better game. Better to innovate than to have the game feel like a massive rehash. Every 16bit Sonic platformer brought something very new to the gameplay. Biggest things Sonic 2 added was the spindash, Tails, and multiplayer. In S3&K, the biggest changes were elemental shields being added, Knuckles was now playable, all of the characters now had their own special moves, the levels were much larger, the level design was now designed around three separate characters, every level had some kind of a transition, Super Emeralds were added, and all of the characters had special forms besides just Super Sonic. While not adding any new abilities is a safe option, not making any major changes to how the game controls would make the game feel much less of a step up compared to S3&K. And hell, look at the media reaction to Sonic 3 & Knuckles. While hardcore fans of the Genesis games usually view S3&K as the best of the bunch, Sonic 2 and Sonic CD are generally viewed as the best Sonic games to the mainstream gaming media. Even then, some people on this site like Sonic 2 way more and really disliked some of the changes made to the gameplay in S3&K. I remember one poster in particular viewed some of the changes as unneeded bloat and felt the levels were way too long. (I disagree with that guy 100%.)
You won't be able to please everyone here, but you're probably capable of making a game most of us would enjoy playing even if we disagree with some of the design decisions. Some of my favorite games of all time have aspects of the games that I strongly disagree with. That's normal. Hell, I'll give you an example. The first three Ratchet & Clank games probably make up my favorite gaming trilogy ever, yet I would have preferred the series to not adept the RPG styled health system was added in R&C2&3. That health system was well liked and had a major affect on the gameplay, but I didn't agree with that design decision because it made the older stages way too easy when you go back to older levels. I don't feel it improved any aspect of the game and it's kind of silly how Ratchet's health system reverts back every game, but my view on that is unpopular and I still absolutely love those games.
When it comes to wall jumping, there's a lot of people here for it and a lot of people here against it. By adding it, you can do new creative things with the level design that couldn't be done in the first three games. For a lot of people here that dislike that idea, I don't think it would completely ruin the game for most of them. Now if it was an ability barely anyone here liked, then it might not be something you want to add but that's not the case. Considering how so many people hate water levels in video games, if Hirokazu Yasuhara chose to not add any water levels in Sonic games because they would be the least popular trope in the entire franchise, we would've never gotten levels like Hydro City and Tidal Tempest. When the Angry Video Game Nerd recently did a retrospective about his memories with the series, all he could talk about when it came to Sonic 3 was how much he hated seeing Sonic drown. I personally love water levels but a lot of people use that Sonic level trope as an example of why they feel water levels suck.
You can only compromise so far without trashing a game's true potential. There's a reason why community based game projects never take off on this site. Best thing Sonic 2 HD did was make it closed project. Worst decision they made was choosing LOst as their programmer. Nothing wrong about wanting community input, but it's difficult to get this site's community to massively agree on anything with few exceptions. Biggest ones that come to mind is the fact an overwhelming amount of the community thinks the spindash and momentum based gameplay are great, and that Sonic 4: Episode 1's physics are garbage.