I had a hard time too when I first tried to get netbird going but reading the https://docs.netbird.io/manage/access-control section of the docs cleared things up, especially the part about not putting all your devices in the same group.

I have Netbird hosted on my VPS, and have my home server act as a routing exit node, as well as the way I access stuff on my home network.

In essence, my setup looks like this

1. Network Routing > Networks, I've set up a network called Home Network LAN which exposes a Subnet for my home network, lit. the IPs I use locally. (192.168...), called Home Subnet
2. Access Control > Groups I have a group called Home Network Users, within which I've put the devices that should be able to access the home network (my phone, my laptop, not the servers).
3. Access Control > Policies sets up a policy called Home Network Access, which has Home Network Users as a source, and the Home Subnet as a destination.

I think that's about it, really. If I am outside of my home network, I connect my Netbird VPN and I can access any and all things on my home network using the direct internal network IPs from anywhere. I have also set up the home server as a routing exit node, and added an Adguard instance as a DNS server so I can use my private network domains as well.

So basically I can connect to my Jellyfin instance either via direct home-IP (192.168.x.5 or whatever) or via jellyfin.home.arpa

I am not sure your travel router needs to be a routing peer.

I am also rubbish at network things, so if you have follow-up questions I'll probably struggle to understand them.

What do you mean "the IP address set to it's Netbird IP address"? In Netbird everything is referenced by it's LAN address.