Really good game concept! The art is very cute as well.
Unfortunately I jumped into the game without reading anything the first time and completely abandoned my egg... I guess I mistook it for a spawn point, egg hatching? (in retrospect you'd think the start screen would have been a pretty big hint)
I somehow managed to unlock the first gate without even knowing I had an egg and then got a game over for reasons I didn't understand. I think it would be helpful if the game over screen was more clearly a game over and maybe explained which loss condition you fulfilled (either death or egg loss). I'm not sure there's a good way to explain the egg concept through gameplay without inserting it as text.
Maybe an intro room that forces you to pick it up to leave (pressure plate puzzle?) and introduces the slime stealing in a smaller environment. (Or a reaction from the player character of some kind whenever the egg gets stolen, like an exclamation point or dialogue the first time; or even an indicator in the UI that shows you whether or not your egg has been stolen so you know it's relevant to you). Of course, those are whole new systems to implement and really I should have just read the premise first😅
I see you have a lot planned for the future of it, I hope to see it! Nice work so far!