Hi there,
Many connections can be added to favourites and automatically added to new projects, but not BIM Cloud connections. Please add to the right click context menu of a BIM cloud connection the ability to favourite and add to new projects. I even tried copying the connection file into the favourites folder in ArcGIS Pro, but it was ignored in a new project.
For example I have crudely photoshopped it in here:

Thanks,
Marc