I ended getting slammed with work, so I wasn't able to do a video review like I promised, but I did wanna still give a good review.
Player controller was good, and the ability to let go of a jump's height early is nice. To further improve the feel of your character I would implement a jump buffer, to make the jumps feel more responsive.
Look into Area of effects for audio. Simplest way to handle it for the scope of your game, would be an area around the player that checks for enemies. If they're within that area, activate them. This will prevent the enemies from infinitely firing off bullets from accross the map. You can also do it the other way around, and have the enemies have their own AOE that activates them when a player is detected within it. Either is valid. Weigh your options. With simple level designs, neither should be too performance heavy. But either solution would be better than it is now.
Also visually making sure the player knows all the dangers is important when possible. As the pit at the bottom of level 2 was not clear enough to be a pit immediately. Maybe add water, since it's a cat, and it has a flaming tail, it would be both thematically, and visually appropriate. Even something as simple as a "fading black pit", or some spikes would suffice.
Lastly on subject of pits, and player overall. I would like to touch on camera movement. Maybe have a camera pan down if down held, up if up held. Especially since you're going to be using vertical level design. You can also make sure the camera follows the player more closely. There are many simple tricks to make the camera do this. You can have the move-speed of the camera following the player tied into the vertical velocity. So falling faster = pan-faster. This would prevent the player from ever falling faster than the camera, and "reaching the bottom of it"; Otherwise it's very hard to tell what's below you when blindly jumping down. Both of these two solutions can mostly address unfair vertical design for the player.
One of the best features and designs of the game was the use of "big cat/small cat". Where the small cat is affected by fans, but can enter small areas. I would definitely lean into that as the identity of the game and focus most of the features around that concept.
Some flair you can add to a future build would making the cooldown timer to be visually shown on the cat. Such as; The tail growing back over the 3 seconds and disappearing when it's not usable. Or have it be less natural and just do a simple bar near the player itself. Since the game is a bullet hell, there's very little time to actually look away from the player up into the top left. So incorporating information into the center near player is a neat trick to address that! :D
Overall a solid 3/5. You definitely have some good ideas here worth expanding on!