This may be a very niche issue, but I spent a lot of time on it and wanted to share my solution. I have a database on an Azure SQL Managed Instance with spatial data (it's not an Enterprise GeoDatabase so there's no SDE schema). I wanted to set up a connection to it from ArcGIS Pro 3.5 using Microsoft Entra Integrated authentication. I had no issues connecting this way from SSMS but when I tried in Pro I would get “Database Connection: Bad login user[ ]”. During troubleshooting we found that things worked when my user was made a sysadmin on the database server but no other combination of permissions would work. Finally, I upgraded to ArcGIS Pro 3.6 and it worked so the issue appears ultimately to be a bug/lack of full support for Entra authentication in ArcGIS 3.5.