I kept coming back to the game for days and being stuck in the exact same spot as you, feeling as if I’d tried literally everything, but I just finally got it after spotting something on this page that made it click and I feel silly.
What to do after getting the green key, if you’re stuck:
(SPOILERS) Hint/nudge
You need to figure out how to push your red key into a door "from the left" to enter the room with the purple key, and retrieve it.While entering “from the left” from within red is possible, no matter what you do, you can’t seem to retrieve the purple key that way.
You need to look for a different way to arrange things to find a door that you can push your red key into from the left, to enter that purple key room.