I saw #23005 got opened for this. Thanks for addressing it so quickly!
On the request for logs: here are the host and client logs from the original occurrence, covering the restart gap: https://gist.github.com/ajbarryiii/7546bdde3a0feb81d4897b1b8ac90488. In short, the old backend stopped cleanly at 07:49:54.5. The remote client started its launch script at 07:49:56.8, and the SSH-launched server took the home before 07:50:02.9. The updated desktop was then refused with ServerAlreadyRunningError on that launch and on every relaunch until I stopped that server by hand.
It's hard to replicate on demand. An update only goes one way, so each attempt needs a new release to install. The remote client also has to reconnect inside the ~8 s restart gap. I'll try to replicate once #23005 lands in a nightly, with both machines on that nightly, and report back.