Hi again,
"Connect to Server" is a part of iOS Files App which allows you to connect the iOS files environment to SMB [file] servers. Quine just happens to provide it since it is standard with the iOS Files App infrastructure, which Quine uses.
What that means is that if you have a local SMB [file] server they can be made visible on iOS. If you wanted to try setting up an SMB server on your LAN, that might be an interesting experiment, as your SMB files should be visible inside Quine via "Connect to Server". I'm not sure how well that would work, as I've not tried it.
My favorite LAN file server solution for working with Quine is SSH using iOS "Secure Shellfish" as a client App. It does a great job of syncing [wiki] files between an SSH server and iOS. You can then find-open-read-write-save those files from Quine. You wouldn't need to run a TiddlyWiki server - just the SSH server.
Does this help?