Most users probably only have a few connections in ArcGIS Pro, but our group manages lots of databases schemas and so we can easily have over 100 connection files. Having these unsorted under Favorites in Pro is a real pain. ArcGIS Pro should have a way to sort the favorites on the context menu along with the refresh.
In the meantime I have created a Python script that seems to work. It takes the favorites.json file, makes a backup and then rewrites to the Favorites.json file with the values sorted on ItemType and Name.
PS: I imported arcpy as I may make this a toolbox in the future so it can be run from within Pro.
Code is in the attachment.