There is one related BUGs that may be the cause of this:
BUG-000126705 - When making a server connection, saved credentials in ArcGIS Pro are not utilized when accessing non-public service and users are prompted for credentials. (Fixed at ArcGIS Pro 3.1)
Not sure of the ArcGIS Pro 3.1 release data but I suspect sometime Q1/Q2 of 2023.