I’ve done similar with an old Android tablet. Installed Fully Kiosk Browser to display the dashboard AND read the battery level - above 75%, switch off power…
But… automations only trigger when going past the threshold once, so if there’s a random issue where HA doesn’t see the battery drop below 10%, (had that happen a few times in the past), then I also have multiple triggers for 5% and 2%… to turn the power back on again 😉
Ah, good call on using the power to get the tablet to respond… I don’t have that problem (tablet freezing), but it does drop off the wifi sometimes.