I need Outlook 365 (desktop version) to do the same thing Outlook 2003 did:

Simply take the address defined at File → Account settings → Change → Email Address as my address when sending email.

As a workaround, I can add the "From" button (through the Options menu) and then change it manually, but that only works for the mail I'm composing. Since it's a hassle to have to remember to do that for every mail, this workaround is unfortunately not practical.

Frankly, I am at a loss why that was changed, and what the point of the File → Account settings → Change → Email Address setting is now, if it isn't affecting my address anymore.