There have been a few (thousand) reports about Outlook not connecting when opening and a "Need Password" message at the bottom of the page, but when you click on it, the password box either appears and disappears, or doesn't appear at all.

Finally you receive an Error Something went wrong [1001] with the only option to close and this repeats itself.

A temporary fix for this has been to go into C:\Users\"username"\AppData\Local\Microsoft\ folder and cut the following folders IndentityCache and OneAuth from the folder, paste them on your desktop and then open Outlook which will bring up the password prompt as if you are logging in for the first time.

Once logged in, cut the folders and paste them back into the Microsoft folder, but do not overwrite the files that have been created with the new login.

I found this works once for a few days, then the problem reoccurs and that fix no longer works.

Having analysed the problem further, it now all points to Microsoft's enforcement of MFA that they pushed out sporadically since May 2023 is causing the issue, as Outlook is trying to re-authenticate, but fails. It seems that where a client has added MFA, but it isn't enforced, there are issues with MFA not functioning correctly.

The fix is for your M365 Administrator to go into the Microsoft 365 Admin console and change the user from disabled to Enable within the Multifactor Authentication settings dashboard.  Once this is done, on the device, go into Accounts - Email & Accounts and remove the email account from there.  Once done repeat the temporary fix to wipe the credential out, and open outlook.

Ideally login to Outlook via https://outlook.office.com and setup authentication again using the Microsoft App.

Open Outlook on the device and setup the credentials for the account again. If it fails to authenticate via the on-screen code on the app, select use a code from the App. Once the code is input Outlook then opens again correctly.

I've tried clean install of Office, adding Registry keys and the temporary fix. All worked for a few days and the problem just came back.  This appears to be the only way to fix it long term.

If someone says start Outlook in Safe Mode...it's a joke as safe mode doesn't change the means of authenticating the login, just narrows down that it's not an add-in causing the issue (which it can't possibly be).

*Update - fix has now been in place for 2 weeks without an issue. Issue is MFA as the mailbox was able to access shared mailboxes which don't require MFA, but primary mailbox was not accessible.