Using Classic Outlook on Windows for personal email, calendar, and contact management
I have the same problem. Using 365 Desktop. I have three Outlook email accounts set up. One from Hotmail works fine. One from my business email works fine. The one created from Outlook has broken search box. While I await the fix, I found that this works for me:
Ctrl+Shift+f
Brings up a search box which is working (it has 3 hard-to-notice tabs for additional search criteria).