I half agree with Serephim's sentiments. Sonic fan games should strive to do more than just give us another Sonic 2 clone with the same plot, the same opening green level, the same abilities and nothing more.
On the other hand, I feel that in order to go beyond what the Genesis titles were, you have to first match them. You have to understand the fundamentals of what made them work. They need controls that make Sonic and friends feel satisfying to play as. Since the controls in Sonic games are often tied to the slope physics, it's also important to derive the slope physics from the real world physics that inspired the Genesis titles. You already know why this is important just from playing Sonic 4 Episode 1.
The games also need interesting level designs that encourage both speed and exploration. Limit the cheap deaths, limit the bottomless pits and dick enemy placement, and instead create challenge through clever platforming and unique enemies with different weak points. Make sure there are little to no automated sections so the control is always in the player's hands. You already know why this is important just from playing Sonic 4 Episode 1 and 2.
Once you understand the fundamentals, you can go crazy and add all sorts of things on top of them. Add in as many different characters, abilities, wacky level tropes and new enemies to your heart's content. You can even think up crazy plots that haven't been done in Sonic games before. But you need a functioning template first. As far as the official games are concerned, the most functional Sonic titles are still the early 2D ones, their only real fault being the zoomed in camera.