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If you look at those links, you will see the first one says "Note: There currently is a limitation issue that will still have you send out with your @outlook address when sending via Outlook. It does work correctly when using the Outlook.com website. You can work around this by adding your other account as a send only account in Outlook."
And it is this limitation (new to the new platform) that is not acceptable. And yes, I have configured an account on Outlook desktop to "Send only" for personaldomain - it does indeed send but the email remains in the Outbox, can't be moved any where and does not appear in the Sent items folder so that old workround which has worked for at east 10 years has now been broken.
Outlook.com Premium is not available for UK and, in any case, I pay subscription for Office 365 which includes Outlook so it should work properly without being forced to buy another sub.
I have now lost track of the number of times I have deleted / reconnected my connected accounts in Outlook Desktop, Outlook Web Access sometimes as IMAP, sometimes as POP3.
It's a continuing nightmare. In the past, I had several accounts, could send from any of them from the desktop, move emails from one folder to the other and all worked. Then they downgraded functionality so emails could not be moved from one folder to another. So sending from the correct and correctly named account became even more important. Now that seems impossible in Outlook and Outlook Web Access.