Thank you for trying it out!
I am still a bit confused about how you were able to get stuck in the wrong rotation, it should not be possible to get stuck in such a way that you cannot fix it by going back just a single room. Can you send me a recording? or a GIF perhaps?
And thank you for telling me how to fix the UI staying highlighted! I wasn't able to find a solution even after searching for around 10 minutes.
After the first rotation room I was able to get past the next one, but the room after (the locked door one) required me to go to a path that was inaccessible because I was rotated the wrong way. The issue was that the room between them was possible even when you were facing the wrong direction. For reference when I entered the locked door room the locked door was on the left
I was able to figure it out after restarting a couple of times so even just adding a restart game button would work well enough if that's the type of game you're going for (maybe add checkpoints too if you make it longer)