If you run two instances it won't obviously fail right away, but it wasn't designed or tested.  I've run single commands while the UI is running though to no ill effect. 

 have fun causing race conditions

welcome to the real world of concurrenc networks 

 this is correct: local state for webapps is stored in the browser, even if you host them locally
i don't think this is easier to sync multi-device than eg gossip's local files

nostrudel does store its settings in a relay-side 30078 event as well, this gives it automatic synchronization of settings between devices, maybe this is enough for what you want 

 yeah, this is also one of the big hassles with web apps is the web browser doesn't easily let you connect the app to a local cache relay... you could then also connect that cache to wireguard and use the same cache on your other devices as well

to do shared state like this you have to build a separate configuration/cache service 

 I haven't tried multi device at the same time, yeah I can image that would mess things up.  I'm closing gossip on the desktop, then sshfs mounting on a laptop and using that.
Now that you mention, I will probably forget to close it on the laptop at some pont and try accessing both at once and get to see what kind of fun that leads to. 

 yeah, since you are linked via ssh just do a "killall gossip" before mount