Thanks.
Hmmm.... I think I need to do some reading up on HTTP Auth. I thought it would store the connection info in a session cookie.
Anyway, thanks to your pointing out I was on the wrong track, I managed to sort things out:
I opened my browser's Dev tools > Network inspector and chose to open the `init?...` connection in a new tab:
which presented me with the login dialogue again. Allowing me to get back into my library:
I don't have enough knowledge of HTTP Auth to work out why this approach worked when reloading the window / bypassing browser cache / restarting browser didn't. But at least it solved the problem. So I'll leave it here for reference, in case it happens again, or anyone else runs into this.