Are you confusing “ports” with “interfaces”? I can see that happening since we do colloquially refer to both as ports depending on context.
Each service will bind to it’s own “port” which is tied up by that service. However each interface (the external physical connection) supports like 65,000 software ports.
So in practice, no, you don’t usually need more than one physical network connection to run multiple services.
I used option 1 (KeePass synced to Google Drive) for years. It’s nice that you know you have control of your passwords at all times, and as long as you can access your cloud storage account and can download a KeePass app, you can get your passwords. It works reasonably well most of the time, but I was consistently running into edge cases that weren’t as smooth as I’d have liked (mostly apps on Android)
I switched to vaultwarden (option 3), and immediately fell in love with things mostly just working. However, since I was hosting it out of my house, I had a bit of a disaster recovery problem. If i had say a fire, I could easily lose all copies of my vault, which would be… suboptimal.
After reviewing the options, I switched to straight bitwarden. I’ve been happy with the experience, and once I have disposable income, I plan to get pro long enough to have emergency contacts available so my family can still get important passwords in case of the worst.
All options have their pros and cons, but IMO password storage is something that deserves to be given proper consideration.