There’s clearly a bad bug here, which prevents db self-healing on startup, which is investigated in your other thread: How do I repair the index database?. That’s why the following doesn’t work for you, but it still applies:
When detecting a fatal error, meaning Syncthing cannot work any more, it shuts down. The web UI is part of the Syncthing service, it’s not a separate thing, thus shuts down too. Then the service manager you use or Syncthing’s monitor process restarts Syncthing. In case of a db error, a check and repair process will happen on startup. In other cases or if that fails and Syncthing crashes again, the service manager/monitor should eventually stop trying to restart Syncthing. Then there’s no web UI available at all, and the user will check the logs and sees the problem there.
What would definitely be an improvement in UX is adding a panic notification to the UI: Have a notification at the top saying that Syncthing panicked, with an option to display a list of panics and potentially even allowing to open those panics, getting the logs and backtraces.