In Pro I went to the project pane and then went to the Databases control where I right-clicked to create a New Database Connection. This database connection (.sde file) was then copied into both the specific user local where SDE files are stored (C:\Users\"User Name"\AppData\Local\ESRI\Index\Connections) as well as the project location that was defined when creating the ArcGIS project.
If I perform this same process manually so I do not have to recreate the SDE connections, I do not see the database connection in the Project pane. Are there some additional behind the scenes operations occurring if I create the database connection in Pro as opposed copying an existing database connection file to the location that appears to be recognized by Pro?
The ability to copy existing sde connection files would be a time saver compared to creating these database connections in the new Pro projects that are created.