I’ve never used CasaOS, so I can’t help you with that, but I run NetBird for remote access to my homelab. What you’re describing sounds to me like an issue I used to have with Tailscale.
I think NetBird might be trying to route your traffic through a STUN/TURN server to get around a NAT or firewall. A NAT (in case you haven’t heard of it) is a sort of “mapping” from one IPv4 address to many IPv4 addresses. Its used to "make more "addresses, otherwise we would have run out decades ago. (this is a simplification, its actually much more complicated)
The first thing to check here is: Are you behind a CG-NAT? (there’s probably some websites to check this)
If yes, then there is little you can do without setting up a VPS to get around it.
If that’s not it, then you’ll have to figure out how CasaOS handles networking internally. Your services might be behind a NAT inside.
As for ressources/information, I mostly stuck to the official docs.
Running Docker inside a VM is the recommended way to run Docker on Proxmox.
Personally, I just run Docker inside LXC containers. Aparently, this is supposed to be not entirely stable, but its never given me any problems. (I commit an entirely different sin against efficiency, by keeping each service in its own LXC container, each with its own Docker host.)
I also run Immich (in Docker inside a container), and haven’t noticed any performance issues. But I’m the only user, and I don’t use it heavily, so ymmv.