This is an outstanding entry, well done. I think with some polish and expansion, perhaps brining more of the emergent storytelling to the front… this could be a decent steam release. Let me start with the best parts first.
First of all I think the pixel art is outstanding, the quality level of the art assets and attention to detail on things like the shader effects is quite exceptional. My only criticism in the graphics department is that the important things (ammo recharge, upgrades etc) aren’t distinct enough from background details.
Being terrible at art myself I’m not so sure what the fix is. But in places like this: 
… the high level of detail matched or exceeded the level of detail of the upgrade stones / ammo refills. Later on in the game this was nowhere near as confusing, once i knew what i was looking for, but early on it was a little bit disorienting.
Overall though i was blown away by the level of artistic detail on display. Unreal that you made something this good looking in a jam timespan.
Next, I really appreciated the innovation on display in this entry.
In terms of the idea “fox with a gun” is pretty cool already, but i also liked the idea that the fox is stuck in some kind of futuristic facility is also fascinating. Pushed around by waves of causation beyond their understanding, with a vague idea that they need to confront and stop the source of the ever pulsating gravity wave… Loved it.
As a game mechanic, “shooting to move” is not as original in this jam, but I think you’ve done something interesting with it, with a set number of bullets and mechanisms to reset and refill you’ve managed to create some interesting platforming physics.
I didn’t like the delay refill when hitting the ground. I would frequently attempt a high velocity maneuver only to plummet to my death when i’d forgotten I needed to recharge my bullets. Getting the upgrades severely reduced this pain point over time, and when i noticed the refill noise it was easier to train myself. But I feel early on it stopped me from “high octane” speed running some parts in a fluid way.
My favourite innovation was the periodic wave. I like the idea of it from a storytelling / ambient perspective, and I like the usage in platforming. Being able to ride the wave with a precision jump felt great, and there were multiple shortcuts available once i understood a layout and could time a perfect wave ride upwards. It also added lots of timing challenge to some otherwise straight forward puzzles.
Finally, I should specially mention the audio / sound engineering. I think there was a lot of subtlety and ambience to the experience which added a lot to the vibe of the game, I also didn’t notice anything grating or poorly mixed. The sound effects felt very polished and professional. Great work!
Next let me address some issues i found with the game. I think the biggest of which is the aerial control feeling very floaty. Perfect platforming physics are ridiculously difficult to get right if i understand correctly (haven’t written one myself since being a kid, but i’ve heard horror stories), and overall for this jam your’s is one of the best controlled that I played.
However I found it frequently very difficult to land my fox in the precise position i needed it to go in, which i think was due to momentum being conserved while moving in the air.
Normally as the source of being airborne is a jump button followed by navigating in the air with arrow keys - the momentum being instantly halted by an opposite arrow makes for smooth navigation…
However in this game that would completely screw up the wave manipulation D:. So I’m not sure how you could add more precision to fix this. Perhaps things like “coyote time” or a tad more acceleration on the aerial movement would give it a bit more crispness, but it’s very hard to say exactly.
Likewise, the green / orange / grey areas were fascinating idea, but slightly let down by their inconsistent behaviour. This was most notable with the grey “launch pad” setups. Where I found that you needed to carefully position your fox right at the edge of the grey square and ensure you ride the fox the entire way along it’s length in order to get the full boost.
Running further into it would negatively impact the trajectory direction, and shooting downwards while inside it would counter-intuitively cause you to gain less total speed when exiting because you spent less time being accelerated within it.
If you decide to ever revisit this project and produce a full release, I think tightening up the physics and platforming should be #1 on the priority list.
Finally, I must confess I didn’t make it to the end. I got stuck here, and couldn’t figure out how to make the jump across to the other side:
The difficulty curve was great for me, and I’m terrible at these sorts of games :( but after many attempts i couldn’t figure out how to get this jump, and the checkpoint was some distance back, requiring a fair effort between each attempt. So eventually I gave up.
I’ll never know if my fox manages to put a stop to the wave or not :(
Overall this was an extremely solid entry, with a ton of polish and love put into it. Very impressive, well done! Continue to grow and challenge yourself!