This is now done and merged - FEATURE: Also allow language switcher to be shown when users are logged in by nattsw · Pull Request #34578 · discourse/discourse · GitHub.
Here’s the video that was included in the PR description showing how it should behave.
Something we may consider is perhaps to retire the one shown in /my/preferences/interface in favour of this one for a better experience where the site owner may choose the available languages for the site. We’ll have a few discussions internally first.