This is probably related to Discourse Meta.
I tried to set in the settings, Backups, allow restore. But it did not allow to save it.
Because there is no error message, I first thought something was wrong with my nginx reverse proxy, showing 405 (Method Not Allowed) errors.
It took a while until I realised that I had set the read-only mode, and that was the reason why all POST and DELETE (user logout) requests failed.
It would be good if there was an error message showing that currently changing the settings or logging out is not available due to read-only mode.