Very clean and very classic indeed! Feels very polished, controls smoothly and plays well. At first I also thought you had remastered a game, which I also get is what you're going for but also just confused me greatly at first, searching the internet to compare it to the original. Part of that is because while I like the remaster mode as a concept, it doesn't feel like the actual gameplay mirrors this. The graphics and music change to a lovingly crafted retro-look, but it makes less sense to me that the platforms would be in different places or would swap around, which for me feels like it has very little to do with remastering.
I'd have liked to see a deeper dive into the use of that theme, perhaps needing to use modern platformer convenient gameplay mechanics like coyote-time to overcome difficulties the 'original' version could not, or changing the way the character moves. Adore the music, also enjoy the idea of picking up concept art, fun to get some more insight into how it's made.
Also props on having settings and re-mappable keys at all!
Some small feedback notes (please view these in the context of having accomplished a great game!)
The original control scheme (S+Shift+Space)is uncomfortable for my hand, it doesn't feel quite natural with the S and Shift being so close. Pressing 5 times Shift on Windows is also a default shortcut for enabling sticky keys, which is unfortunate.
When using the staff for jumps near walls, sometimes the character would cling to the wall a little too easy.
The triple jump feels great when making horizontal distance, but due to having to hold it longer for higher jumps it doesn't feel as satisfying to use for making vertical distance, usually only reaching about 0.8 times higher than my original first jump using all 3 extra jumps.
Some even more minor things: The whole game is keyboard-controlled, but the menus are mouse controlled. The menu also immediately told me I had to switch to remastered mode to see the extras, but I hadn't even learned how - Perhaps this text could only be visible in the retro menu.
The 1controller2games and streaming menus were a bit lost on me. Many remastered games have this option, and it doesn't really feel like you're playing 2 games at the same time, but switching between them. This would have made more sense to me if both were visible at the same time taking the same inputs (which could be a mechanic all on its own!)
All in all a great entry to be proud of, congrats to everyone on the team!