Thanks for the detailed report, Anatol. I see this as a feature request, but I do understand the confusion that a user encounters when seeing the site in one language as an anonymous user and another language once they are signed in.
We could use a site setting here that enables saving the user locale based on the browser/OS setting on signup. Currently, we only have the “set interface language for anonymous users from their web browser’s language headers” setting, which is clearly for non-authenticated users.
Marking this as pr-welcome, we don’t have bandwidth at the moment to take on this work, but happy to see it happen.