I had a 4G modem with a web interface many years ago. It was flaky and would often hang. I just had a raspberry pi on my network pinging some known address, if it failed for long enough it’d replay the commands to restart the web interface.

If I’d have the same problem today I’d probably have home assistant power cycle the router with a smart plug.

homeassitant access would require internet wouldn't it?

Nah, you can use an HA Ping (Settings>Add Integration-> Ping) trigger against 9.9.9.9 or whatever and run a script if it comes back false for X minutes