Symptom: Clicking in the Search Box of outlook doesn't work, cursor won't stay put. BROKEN.
I believe we were all chasing our tails, I don't think the problem is the windows indexing nor is it the outlook desktop app. I think it is a caching corruption in our Microsoft accounts. The reason I think it is the account and not the software or operating system is because I tried almost everything in the past two days.
- Indexing Options: rebuild the index
- Repair Outlook via windows settings, installed apps, modify
- Uninstall / Reinstall outlook
- Upgrade in place (clean install of windows and preserve data) with brand new copy of office 365
- Grabbed old unused laptop from work that I never logged in to before, downloaded NEW windows installer, added brand new copy of office 365
- STILL broken!!!!
- The only way I should see the same broken feature on a brand new machine is if it was a universal bug that every single person was experiencing (which it is not) or it had something to do with my Microsoft account
- As I was installing windows, the outlook app on my iPhone was also acting up and not autofilling addresses in the TO fields. This was when I was when i realized this headache was all related to the Microsoft account
Click your Account Icon from the top of your desktop Outlook App, click My Microsoft Account

Click on the Privacy icon on the left (you will need to authenticate again), then click on Browsing and search

I left browsing history alone, and clicked on Search history, then CLEAR ALL ACTIVITIES

My search box is now working on all my devices again.
I think clearing the search cache in the Microsoft account did the trick. It took me 2 days and a spare computer to do it.
I don't know how fast the fix took after the clearing, but it wasn't instant, it could have been 5 minutes or 1 hour, (it was unattended so i'm not sure). I assume microsoft azure or whatever controls the Microsoft account ecosystem must take some time to replicate the change to the devices.
What i'm saying is if it isn't instant, close and re-open outlook again in a few minutes and see if this did the trick. Anyone else still stuck, give this a try and post a reply to let others know i'm on the right track.