Yesterday I had the exact same problem, after the dreaded “your packages are outdated. Please re-login” dialog showed up during a flight.
I believe that the problem is related to the native screen resolution vs the actual game resolution. In my case I have a monitor (well, an iMac ;)) with a native 5k resolution, whereas I set the FS2020 game resolution to FullHD (1920x1080). My guess is that the actual XBox login screen that is supposed to show up after clicking on the “Sign In” button is placed somewhere off-screen (it is supposed to be “centered” on the screen, but possibly wrongly calculating with the native screen resolution instead of the effective “game resolution”).
In any case this is a known problem since almost day 1 and a workaround exists as well, which worked for me just now:
https://forums.flightsimulator.com/t/xbox-login-screen-stuck/145046
After temporarily renaming your local FS2020 installation folder (somewhere in your user folder, depending on whether you have the Steam or Microsoft Market (?) edition) the installation screen appears in the “native resolution”. And in my case the XBox login screen was centered, but tiny (e.g. not properly scaled: fonts were almost unreadable small etc.). Which leads me to the educated guess that when the loading screen appears in a much much lower resolution than the native screen resolution the XBox login dialog is then “centered off-screen” (using the native resolution as basis of the “center” calculation - but again, just a wild guess).
I have created (yet another) ZenDesk ticket about this and will try to amend it with this information (which may or may not be of help to the developers).
UPDATE: Interestingly @brotbuexe4206 (who gave the valuable workaround, thanks!) also mentioned that he “… reduce[d] the “interface scale” to 60. This already works at the login rompt. Maybe this is causing this issue.”. So this really sounds like that the “visibility” of the XBox login dialog (which seems to be rendered “on top” of the FS 2020 login screen, in native resolution) is related to screen resolutions (or “ratios to the native screen resoltuion”). Some “center dialog” calculation really seems to go “off the charts” here…