How did I find this? I don't know.

The bug

Upon logging out and then logging back in of a Mojang account while a Microsoft account is logged in at the same time, the Minecraft Launcher enters offline mode for a few seconds after signing in (around 30 seconds during my tests), until reverting back to online mode.

How to reproduce

1. Open the Minecraft Launcher (connected to the Internet)
2. Make sure you are signed into a Mojang account and a Microsoft account
3. Log out of your Mojang account from the dropdown menu in the top left corner of the screen
4. Click Add account -> Mojang Login -> sign into your Mojang account
   Notice how the Minecraft Launcher appears in offline mode for a few seconds, before switching to online mode by itself

Additional information

This was not an issue in 2.2.910; this has been introduced in 2.2.1166.

I have set the Environment field to macOS, as I have not tested on a device running Windows yet. I have, however, tested on two different devices running macOS (10.13 and 11.1), and have received the same results.

Yes, the Microsoft account needs to be signed in as well! I could not reproduce the issue when the only account signed in was the Mojang account.