i like the wallclimbing, and how the limited dashes make it important to decide when to use them (i'd like some indicator though to tell how many dashes i have left).
the respawn is kinda inconsistent, with the wall of spikes only occasionally resetting and many moving obstacles dont reset their position (which can make some jumps almost impossible when paired with the camera). i think you should do some additional checks to make sure the obstacles are properly reset when you respawn. also, the fact that the jump doesnt reset during respawn can lead to you getting softlocked when you respawn right into a spike placed above at certain checkpoints. of course, this might just be a problem with my browser? we'll see how others fare.
you should probably code the camera to stay in front of the player's direction to help mitigate leap of faiths (or maybe zoom the camera out a bit? idk).
finally, this is probably just skill issue but i find the hitboxes a tad big. depending on your intent with the game, you might want to shrink the hitboxes to make them more forgiving (this pairs well with the wall of spikes urging the player to move quickly and make riskier plays to stay ahead)
bugs and camera aside, this game plays pretty well, and the gym theme is well-integrated into the mechanics