Hey I love your game and I honestly think it's very adorable but I just wanted to recommend a small improvement I think could be easily made! That being the fact that you have to stay in game when she sleeps to restore her energy.
I don't know if this is only a thing I'm struggling with but when I try to leave the game open in the background with her sleeping to restore her energy, the game sadly doesn't register the fact that she's still sleeping and therefore her energy won't get restored. This might be in the long run a bit annoying when I just wanna go to sleep without having to worry about my battery running out due to me still having the game open.
Another solution (which might be more time consuming though) could be to just add a minigame to occupy yourself with whilst she's asleep. The first thing that'd come to my mind when thinking about minigames that could fit the vibe of the game was a simple flappy bird like game but instead of the bird it was her bat form! :3
Once again, I enjoyed your game a lot and am looking forward to the improvements it could still make!
Best wishes <3