Yeah, that's my PC, the one running the server. I tried those open port checkers and they said that the AC ports, and every other port for that matter, are closed. Like, all of them, including ports that I know are in fact open, like the one being used by my browser.
Well, I just tried the scanner at
https://dnschecker.org/port-scanner.php on our own server at avon.racedepartment.com, against ports 9702,3,4, where I know there are servers running and answering on ports 9702 and 4. The port scanner reports that 9702/4 are open and it just times out on 9703 (which is not unexpected, since nothing's answering).
Some firewalls will actively reject packets they don't like (allowing a port checker to report "closed"), but these days firewalls will more often than not simply bin them.
Not sure which result you got. If it was genuinely saying "closed" then you definitely have either your PC or your router rejecting the packets. If you tried it with the AC server not running, then a timeout would be consistent with everything being configured OK (e.g. Avon has a firewall rule to allow packets to the server on 9703, but it simply isn't running today). It's only if you try it with the AC server running that the port scanner will be in with a chance of reporting that the port is open.
Ports used by your browser: not sure what you mean by this. Your browser will for the most port only make outgoing connections, for example to port 443 on a https site or 80 on a (now unusual) http site. That doesn't require any ports to be open because you aren't running a server within your browser. Maybe you mean something else though?
Modern routers are capable of a certain amount of "automatic" port opening (and are often configured out of the box to do some of it, the security of which is debatable) for certain scenarios that require incoming packets to be able to get through that
aren't associated with an existing TCP connection that was initiated from the inside to an external host. I don't think that's what you are likely to be talking about here though.