Sounds like your container has some kind of side-car that makes it directly addressable over Wireguard without needing to address the host IP. Does that mean you'd need to modify the docker-compose in some way before `docker-compose up`?
How do you know which port Paperless is using for HTTP? When you want to load up Paperless in a web browser, are you typing in a service name, or the container IP address? If it's a service name, how are you doing DNS? Do you have TLS?
Not necessary. You can access the deployed docker container without exposing any ports or having any reverse proxy (what you've likely thought about with sidecar, which is a k8s concept, not docker) or anything else by using the ipadress of the started container and the ports the started service used. This is usually only possible from localhost, but wireguard can be configured as what's essentially a bastion host and exit node, this would let connecting clients also address containers that were started on that server, without opening any ports.
You can technically also do that without wireguard even, as long as you configure the docker host to route relevant traffic into the docker ethernet and define the docker subnet as a static route that points to the docker host, but that's another story
For services open to the public internet I just add a subdomain + a reverse proxy entry into an existing caddy instance and point to the docker IP.
Your explanation is interesting though. Would that actually work?