If you get complaints about the difficulty, that doesn't mean there's something wrong with your design. This is top grade level understanding of platforming and level design and all that's needed IMO are small tweaks and tricks to make it a little less frustrating to spawn back at the beginning. Because you should keep spawning at the beginning, that was actually a great choice.
The only thing wrong with the difficulty is the curve, it's just a short game condensed in a short time so how can you avoid that? The world did an amazing job at teaching the mechanics and there is thought to every aspect of the character movement. This is proven in the level design, as there's a puzzle for everything in your skillset. You don't always need to be "nice" to the player, some of the best games ever made thrived on the sense of achievement after a lot of work, they thrived on being "tough but fair".
What many may not notice is all the small things you did to make it easier for the player, the very lenient hitboxes, the super-predictable jump length and height, the order in which things were introduced. Saving moving platform for late in the game, which is such a common and spent mechanic, was also smart. Those were one of the most difficult things to deal with in the game, they threw off your rhythm and forced you to react and improvise, and would only be in the way early on when the player was learning the skills.
There's some butthole-tightening hard areas to get through, but for some reason I rarely died in this game. The controls were airtight, it was 100% down to your own skill and no jank. I have no idea how I managed to get through that "hell" part, but after that I had to walk away from it for a bit.
I love how your own jump becomes the "skip" mechanic, the further you're into the game the faster it is to get back to were you were, even though it's further away and full of dangers. Learning the map was an engaging part of the game, it could have needed some slight variations to the visuals to distinguish the areas (for memory), but nothing too crazy. I don't think you should add checkpoints, but try finding other creative ways of letting the player skip with their skills, , at least only do so if you increase the scale of the game.
I'm going to say that the theme works as well. It's not so much the character that's evolving, but the world and how you traverse it. While nothing has physically changed, it's a completely different place when you're zipping through it on a streak of blue light.
Can't tell you enough of how impressed I was by your design decisions, and I'm tempted to tell you to ignore some of the comments you might get about your choices in pacing/difficulty/design and go with your guts. They seem to be working.