Using Outlook for Android for personal email and calendar management
Could you please clarify whether these accounts are already listed in Outlook but appear disabled, or whether the endless loading occurs while attempting to sign in and add them? Also, can you successfully access your personal mailbox through https://outlook.live.com?
Finally, when you select Activate an account, does Outlook display a Microsoft sign-in screen, request authentication, or simply remain loading without displaying anything else?
One additional possibility worth investigating is the interaction between Outlook and Microsoft's authentication applications on Android. Microsoft documents situations where Outlook cannot complete account setup because Microsoft Authenticator or Intune Company Portal is restricted from running in the background.
Additionally, please also attempt using a different network.