Is there a way to run a browser window within HA?

Again, they do sell such things. HA is great, but sometimes we want it to do things that other hardware already does well, reliably and inexpensively.

The Shelly plugs can auto on, when off.

You could also programm a esp based device through esphome to do the same.

Esp32 with a relay attached

I use a z-wave power plug, so that when wifi is out, HA can still issue commands via the z-wave USB dongle that is on the HA box.

Or use a smart plug with ESPHome / Tasmota / Shelly - those plugs could have simple logic on the config/firmware of the plug itself, so that you donā€™t have to rely on wifi.

Why wouldnā€™t you be able to run a shell_command with a script? Execute curl commands to auth and trigger the reboot?