This is rad!
Just played the first few levels of the web build.
Impeccable visual polish on the animations - the spherical motion and the motion blur trails on the stars in the "sky map", the transitions into and out of puzzle mode, the springy easing animations on rotation and such... Plenty of fantastic touches all around.
I feel your pain re: pico-8's two-button controls but I will share my experience with the controls regardless.
Much like another commenter, the puzzle mode controls are taking me a lot of time to adjust to. The "shift key" actions on Z and the "grab/drop" on X feel exactly backwards to me. I would expect Z grab and X as the "shift key." D-pad-up instead of the grab/drop button as the "select from inventory and grab" input was unexpected, and X+down to put a block back in my pocket was also a surprise. I wonder if there is a way the "shift key" could work like the PS3 "cross media bar" - up/down to cycle through a list of blocks - one of which is an empty slot to put the current block away - and keep left/right to rotate or reduce to one-directional rotation direction on press.
Progress should save on final polyomino placed, rather than on exit to menu. I had to reload the page to log in to leave this comment right after completing a puzzle and I came back to find the puzzle marked as incomplete again because I hadn't proceeded to the map screen after completing the puzzle.
Minor: you should disable key-repeat on the X grab/drop button. Once I held the button down in a "click and drag" fashion which resulted in the block being repeatedly grabbed and dropped.
The custom pause menu is cool. I didn't know it was possible to intercept the p8 menu button press.
I agree with another commenter that the perspective effect feels too dramatic.
Audio sadly wasn't working for me on the web build. Chrome was indicating the tab was playing audio but I couldn't hear anything.
I couldn't play too much today and I want to come back and play some more soon!
I have my own polyomino puzzle-type game called Sticky Chunks I've been developing and would appreciate feedback from a fellow blocks-enjoyer. I hope I don't come off as if I'm using your comment section to self-promote, but check the links on my personal site https://timromero.games if you'd like to play it or to email me. I feel like there is at least one UX feature I came up with for it that you might consider copying.