Just finished playing, though I didn't quite complete it - stuck on 248 purple things (what are they called anyway?). In general I like it a lot, I can definitely see the PS2 platformer inspirations! Here's some feedback.
-Breathing fire on things made me think of Spyro on PS1, which I played to death when I was a kid. They way the purple things are distributed in the level also remind me of the gems, with most being easy to pick up and some being trickier. In general, those work really well to get you to look around and fully explore the level and the mechanics. With Spyro on my mind I did miss the old l1+l2+r1+r2 trick to find the closest one, though I guess I did see them all in the end anyway. A small touch I think would work well is if they start vibrating slightly when you're close but not quite in pickup radius, otherwise they are great.
-The jumping. It works alright, but when it's the central mechanic it should be great. It's a bit too slow and floaty. When I jump I want there to be a proper upwards movement immediately, with the longer/double jump being a bit of an extra boost once I'm already in the air. As it is now, tapping the jump button makes a jump so small that it wouldn't accomplish anything and is pretty unsatisfying. I have to hold down the jump button for a long jump every time, which makes it pretty pointless. The hold for longer should be a small bonus to a normal jump, not mandatory every time. The double jump has similar problems, but to a lesser extent.
-Alternatively, make the jump smaller and let us grab ledges. Since every jump is towards a platform it would work out the same difficulty-wise. It's very satisfying to just barely make a jump, grab the ledge and pull yourself up. Now you instead have the experience where your knees hits the ledge and that means you fail. It works in Spyro because he doesn't have arms and in Mario because he's so short, but Pumk is basically human-shaped so you expect her to have more human movements - like Jak.
-Pressing Y on the signs instead of A felt really strange. It's not inherently wrong, it's just different from how every other game does it. I guess you might not want to block the player from jumping because it would start reading the sign, but I feel you could get around that with the level design.
-The signs themselves were good though. Maybe a little too many, but they're funny so it's fine.
-I like breathing fire on a checkpoint to activate it, you get a feeling of progress. But it's annoying when you're running around the level for collectibles, fall to your death and respawn at the opposite end of the map. How about if you light up a checkpoint to activate it, and when you die you go to the closest lit fire?
-The camera prevented me from looking up as much as I would have liked. By itself that would have been fine, but sometimes I would have to back away so I can see collectibles that were above me.
-Pumk looks really cool. The design is good, and the model works very well. Even little details, like that her head has a fire and so it glows and so you can sort of see where you are when you're in a bush. Also good animations. No criticism here, it's just great.
-I like how you can throw Alley at enemies and obstacles, but it's never necessary because there's always a rock nearby. I feels like a mini-moral choice, except mostly silly since Alley feels indestructible anyway.
-Speaking of Alley, I like what she's about as well. First time you control her it's slow and plodding, but that's actually good - it feels like the movement matches the character, and you don't actually need more in her areas. Only two suggestions is that selfie cam is slightly more zoomed out so you can see a bit more of the background (screen should still be 80% Alley though) and that when she teleports in it happens off-camera. It's a bit jarring now.
Finally, not a criticism but how do I get the last purplies? I know where they are, it's on top of the rocks where you burn your first bushes, just before the first checkpoint. They're up on the right, but how do I get up there? I've tried everything, I've spent more time on this than the rest of the game combined and I feel like a pirate with a steering wheel in his pants - it's driving me nuts!
Anyway, can't wait to see what comes next.