I've been successfully running https://tube.jeena.net from a NUC in my kitchen now for half a year. It has its downsides, for example when I'm not home and something happens to the NUC so it can't be remotely rebooted then I need to wait until I'm home or sent someone to do a hard reboot, which happened now 2 times.
But overall I'm very happy about how well it works to host from home. The NUC only uses about 5W and it's not super powerful but I don't have so many users on my websites. I'm actually thinking about moving other things from the Hetzner server to that NUC like Nextcloud, TT-RSS, Mastodon and perhaps even this website some day. That would be the ultimate thing, hosting everything on my own hardware.
You can set it up with auto boot after power is provided and then use a remote controlled outlet. Depending on where you run homeassistant, you could control it though there or use another service for this particular outlet.
Funny story I run HA on the same machne ;)