I was struggling with this since Pro was released. I even created a support ticket for it. What we came up with was basically turning it off and on again. To get it working I did the following:
1. Under Project - Options - Indexing
- make sure the following are checked on: Use index for searching, Update the index periodically, Update items in the index every 1 hour (or as you see fit), Reindex all items from scratch every 60 days (or as you see fit), and, most importantly, Index items on network disks. Double check to make sure that the "Skip enterprise database connections" is NOT checked.
2. After confirming those options I had to uncheck the Use index for searching, hit ok, save the project, close the project and re open.
3. Go back into the index settings and recheck on the Use index for searching.
4. I then had to kind of force a reindex by setting the Reindex all items from scratch every day starting at one minute from now and hit OK so I know it's reindexing immediately.
I gave it a good 15 minutes to reindex my drives and enterprise geodatabase. We don't have that much compared to larger organizations so the indexing process could take a while for some and be relatively fast for others.
I've noticed that if I create a new enterprise GDB connection (like to a different version or as a different user) Pro will need to reindex to find featureclasses in it. I've also noticed that it likes searching metadata and tags so it's important that your data has those.
Indexing Options