Using classic Outlook for Windows in business environments
I have multiple email accounts and the only way that worked for me was to set my primary email account first, then remove other accounts (as necessary) and re-add them. They will stay in the order added.
Procedure:
Click on the three dots next to primary account, choose "Manage account". In the new dialogue screen, click the Manage button against your Primary email and click on "Set **** primary account", follow the process.
After restarting Outlook, click on the three dots next to primary account, choose "Manage account" again, but this time choose to Remove accounts between your Primary and what you wish to be your second.
Now after having your Primary, second and third ... etc ... in order, click on Add account" below the email accounts (or wherever you have it) and start adding other emails in the order you wish.
I was afraid that it will delete emails and to reload them again, but luckily, it went seamlessly, as if I was removing a title and re-adding it (it did not even request login details!!)
Until Microsoft sort this one out, I hope someone will find this workaround useful.
Good luck, Simple.