Ubuntu uses a service, Network UPS Tools (NUT), to monitor UPSes and take given actions when they send signals.
The Eaton 5e is not a network UPS, its USB. This is what I needed to do to set it up.
$ sudo apt install nut nut-client
For whatever reason, I didn't have USB libraries on my install of 24.04. So:
$ sudo apt install libusb-1.0-0-dev