@Uzie . I can't explain the different operation you have noticed. You could try Wireshark to capture what happens on the direct internet connections which stop working.
The ports 500 and 4500 are things your work computer connects to at he work end. They are not relevant at your end.
On work computer, do netstat -an
You should see ports 500 and 4500 with your work address. Port forwarding is not needed.
Regarding the last nmap, the Sagemcom has no port forwarding rules and the ports are not open on either of your computers. They are seen as Closed.
