I've never played a Mario & Sonic game, and I'm not an expert on Sonic lore, but there's so much potential to be had here! I wonder who thought up of the Olympics idea…
I have some ideas for a non-Olympics game:
It could be a 3D game where you can play as several characters from both franchises (Probably a combination of Super Mario Galaxy and Sonic). Elements from both Mario and Sonic games could be incorporated (Collecting things in Mario and speed in Sonic for example).
An RPG featuring both franchises. It could be like Mario + Rabbids where the gameplay was something that had not occurred in the past for both franchises (Tactical based gameplay for example). This could be amazing if done right.
It could be a 2D game! Nothing like a classic side scroller eh?
Like I said, there's lots of potential! Heck, the soundtrack could be composed by Koji Kondo and Tee Lopes!
Side note: I find it funny that Mario and Sonic casually compete in sports together, while Mario and the Rabbids must save the galaxy from corrupted cosmic entity.
put sonic in the mushroom kingdom and mario in idk, mobius/south island/green hill/whatever you wanna call it, and pull a sonic generations by giving both characters their own unique playstyle