This is a neat idea, and it could be a fun game with more polish.
In the end, I stopped playing because I was feeling lost in the game. I found the plug in the other room, but then did not manage to explore more without running out of power, and I gave up after 15 minutes or so. On the first couple of runs, when the screen went dark, I was not sure if the game crashed or froze, or if it was part of the game. Since there wasn't anything I could do (and since it happened when I was hidden under a chair), I just assumed that the game crashed, and restarted it.
After a couple of trials, I found that I can still access the menu - and still didn't find anything I could do in this state, so I started optimizing my search and looking for another plug to charge the phone, but did not manage and finally gave up.
Perhaps, from a gameplay perspective, it would make sense to start the game in a more linear area, where the player could try out all the mechanics with some hand-holding, so that they knew what to expect before entering the house. Another thing that would help is a battery + signal strength icon permanently on the screen, making it look like a phone screen. That would warn the user that they need to start looking for a plug or backtrack before they get stuck.
With this fixed, this could be a fun exploration experience.