The built-in Updater binary sensor does not declare a device class. This is used in a few places, including in the Lovelace UI for setting the icon pair used for on/off states.
I’d suggest the
problem device class, given that the updater is “on” when an update is available, and that this is used in other Updater-esque devices.
This should be a simple change of components/updater/binary_sensor.py to override the default