If you do a forward high jump and let out of the forward input while the player is in the air, he still keeps moving forward until he hits the ground. This can feel a bit annoying at times when you want to land on the platform that is below the player. Now that I'm getting a closer inspection, the air control is mostly fine except for the detail I've mentioned above, but there's also the fact that the camera has no smoothing, which makes really weird to control him while airborne, try jumping and changing directions while in the air, you'll notice that the camera snaps left and right instead of one smooth movement.
These are all details that can be enhanced to make your overall movement feel better, and its what great platformers do:
Oftentimes, great movement and controls are resumed to many little things done well, so I'd suggest seeing how other games such as Celeste does. The problem that I have with Contra is that is too old and "digital" movement, which is pretty outdated. Players nowadays want to feel natural and smooth while moving their characters, so definitely check out how great games do their movement.