Using Classic Outlook on Windows for personal email, calendar, and contact management
I have an outlook account with my university (no advertisements) and the message navigation arrows in that account are now missing there too.
In case it's not yet been mentioned, ' Ctrl . ' works for navigating to the next message and then ' Ctrl , ' works for navigating to the prior message. That is Ctrl period and Ctrl comma work for navigation. I've found these keyboard tricks to work for both my free and university web-based accounts.
Hopefully that will be helpful for now.
Microsoft, lots of us have other things to do than find work-arounds for your programming shenanigans.