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.
They do scan and try all ports.
I have a tiny VPS as reverse proxy with SSL termination for my fiddling. That one has a wireguard network to my hardware at home to which it forwards some hosts.
The tiny VPS is definitely the bottleneck in the equation, and if I were to have loads of traffic I’d probably go with cloudflare or -front in front of it.