The puzzles are wonderfully designed! It's been a while since a game actually made me think! It reminds me a lot of those really old school Zelda games from way back in the day! Great job!
However, I think that only holding one key of a colour at a time doesn't really add anything to the game and actually creates some moments where you have to needlessly backtrack, like in the 2nd last puzzle.
With the nature of how the puzzles are currently designed being only able to hold one is more of an hindrance rather than an interesting design decision because it's not really necessary. If you were only ever able to hold one key of any colour at a time then it would correspond better with the theme.
That being said, I don't think it's a bad game. I think the puzzles are great and fantastically designed, but the theme wasn't integrated that well.
As someone who isn't very good at coming up with puzzles as you saw in my game (https://bigfraudbigfraud.itch.io/gmtkjam2019), I have mad respect for the puzzles you have here because I wouldn't have been able to come up with anything like that myself!
Great job!