Web UI does not log out the user automatically after the session expires

[gzdunek]

Web UI used to log out the user when it detected that the session is expired.

This what happens in dev tools (looks like we try to log out the user):

I suspect this can be related to #43071.
Previously, we ignored any errors from api.delete() in session.logout(). Now, we redirect to the login page only if deleting the websession succeeds (which does not).

As a result, the user sees a 'missing session cookie' error everywhere in Web UI, and even clicking Logout has no effect.
The page needs to be reloaded manually with Cmd+R.

[gzdunek]

cc @rudream this may be related to the linked PR.

[zmb3]

Let's add an item to the test plan for this as well.