It likely already does "the right thing" according to POSIX. tmux starts a server and then immediately connects to it a client. The server portion is what's b

It likely already does "the right thing" according to POSIX. tmux starts a server and then immediately connects to it a client. The server portion is what's being erroneously killed. Starting a server is a relatively normal thing, and one of the steps is to create a new session. setsid() is how you do that. Systemd shouldn't kill processes in a separate session.