Neat puzzle!
Think you should set the embed size to something smaller, the game could easily fit on the screen even without having to go to full-screen, many people use smaller than FHD screens. Since you are using Godot, in case you developed the game for a fixed resolution, you can try setting the window scaling in Project Settings / Window, this will let the game stretch to whatever size while keeping the layout and relative sizes of elements intact.
Using Escape instead of Tab for the menu would make it more intuitive.
Would be nice to see errors on the current board state.
The font on the rules looks cool but it’s a bit hard to read.
The music was cozy!
The “dropping rule” confused me at first but it’s definitely an interesting one to think about.