I had this issue twice in the last 3 months. The first time no one really knew what was causing the issue, but my SDE database connections wouldn't load any data. You would connect to them but in the Catalog, when you opened the drop down it would be empty. My IT department basically redid my computer since they thought it was related to my Windows User Profile. The problem was fixed at this point but was a huge pain.
Yesterday, 1/29/2024, the same issue happen. All my SDE database connections were in Catalog, but were empty all of a sudden. Thankfully, I found this thread and believe I found the issue as to why it happens. The problem only started after I enabled Indexing for Enterprise geodatabases in ArcGIS Pro. I just disabled this index and my databases load all of their contents.
@LaurenWinkler @Anonymous User @LarryMcEvoy70 I would disable Indexing on Enterprise geodatabases on your end and see if this resolves things. Hope this helps!