The new Outlook (Monarch) licensing hugger-mugger
I wrote previously about the new Outlook client and have been using it since that time. It's fast and fluid, but it leaves much to be desired in certain specific workflows.
Another thing I missed, but a colleague of mine, prompted me: the new Outlook app for Windows – codenamed Monarch – will not initially work unless your specific accounts are appropriately licensed on the Microsoft 365 side.
This is a bit tricky, and I'm cutting corners here just a bit, but the initial limitation with the new Outlook app was that you had to license your email accounts for Microsoft 365 Apps to be allowed to add said accounts to Outlook. Thus, if you had a work email properly licensed (say, Microsoft 365 E3 license), it was all good, but then when you added your hobby account, which is licensed for Microsoft 365 E1, you couldn't do that - as E1 will not allow you to utilize Microsoft 365 Apps, such as Outlook.
However, this has worked for an eternity with the classic Outlook, and I believe Outlook on the Web also.
This is fixed with the latest update to the new Outlook - available since early February 2024.
Go to Settings > Accounts > Email accounts and select the Primary account with a proper license, such as Microsoft 365 E3 or E5 (or Business Standard/Business Premium or similar). The other accounts will then work.
On my grandfathered (from preview), the new Outlook app doesn't show this capability:
And yet, everything works as it should. Fresh installs, however, will show this new capability:
The current version, where everything works on fresh installs, is 1.2024.223.300.
Additional resources
For more details and background on this issue, see the following feedback item: https://feedbackportal.microsoft.com/feedback/idea/2f7925cb-3a80-ee11-a81c-000d3ae46fcb and the link in the comments points you to the updated Microsoft licensing detail post: https://techcommunity.microsoft.com/t5/outlook-blog/how-licensing-works-for-work-and-school-accounts-in-the-new/ba-p/4047361.