This was great! I've only gotten to the platinum time relic for now and I just gotta say you nailed the look and animations of what classic Crash is. I really liked the circle pointing to where you'll land out of Crash 4, it was refreshing seeing you didn't just look in the originals for inspiration, a lot of proyects can be seen very solely inspired in the past to make something new and I'm glad that, while this does rely in the past aesthetics of the franchise, it doesn't really solely have to play like them entirely. I also enjoyed the implementation of the camera and how it switches from the classic hallway to 2D!
That said, I think the controls aren't quite there yet, while I do like the implementation of the double jump seen in Crash 4, as (for me) that's the best a Crash game has ever played, I feel like the controls are a bit floaty. Like think for example the death animations or how you fall into a pit, it's really fast, that would give you the impression that Crash/Coco have some weight that just isn't there for the rest of the gameplay. I don't know if it makes much sense explained like that, but it's the only comparison in game I can think of to display how the weight feels a bit inconsistent. It does feel floatier than Crash 4 and not as weighty as Crash 2 or 3 (Crash 1 is way too stiff and heavy for the kind of gameplay you're implementing here and that's completely fine). As another comment put it, it also feels a bit slippery, which exacerbates the floatiness of the movement, that's probably the most pressing issue.
Overall great work on this! I'll be looking forward whenever you decide to update or share progress!