Pretty good for your first game. I think the game could use a bit more user feedback. There's actually 2 approaches to consider (imo):
- Introduce some outline effect for things the player can interact with when near. This can kind of help against the player just walking and spamming but I also think it can reduce the player wanting to explore as they won't look at the levels but just the highlight
- Do how old games do it, and indirectly guide the player to it. For example in half life there was a rocket. Nothing was telling you to launch that rocket but as a curious player you just want to launch the rocket, so you look for a room that contains launch control and you just press the button, and it works.
I had this with the cake and mouse. It just made sense so these kind of interactions are really nice. But the shower was a bit harder for me because I couldn't distinct the shower switch from the background, so I just walked around and clicked everywhere. If you are more deliberate in guiding the player by making it pop out I believe it will improve their enjoyment (but avoid the yellow paint problem, were you quite literally tell the player just do this).
All in all, good job on this!