Disclaimer: I understand that nowadays one can expect problems when attempting to start a Thinlinc session on a machine where a local session is already running for the same user. Hence the “Not Thinlinc” tag. 
Still, as far as I can tell, this set-up works for me on Fedora 43 + i3wm when connecting from outside the local network.
When connecting from inside the local network however, this only works if I keep port forwarding enabled on the router: If I disable port forwarding, I get a connection time out.
The session gets created: ps shows a tl-session process, the admin panel shows the session, and neither vsmserver.log or vsmagent.log suggest any problem.
If I diff the xinit.log of a successful vs unsuccessful connection (i.e. with port forwarding enabled vs disabled, respectively), the only meaningful difference is the following line, which shows in the problematic session logs only:
Timeout waiting for smart card tunnel
While that surely looks relevant to my problem, I’m having a hard time seeing how disabling port forwarding can lead to this…
I’m not using the smart card feature, and I can ssh into the machine without a problem.
At this point it’s merely technical curiosity, but if someone has the beginning of a good explanation, I’ll take it! And maybe the discussion will be helpful to other multi-session abusers out there!