Catalog in ArcGIS Desktop has an option to "Return to last location when Catalog starts up".
This allows you to close ArcCatalog, do whatever needs to be done such as installing Windows Updates, and then return to where you were when Catalog is opened again. We're always using this feature.
You can set up a "Data Management" project in Pro to replicate a small set of the expected ArcCatalog abilities but there does not appear to be any way to close Pro and then return to the same job/work location when opening a project at a later stage.
First Prize would be to have such a setting available per Pro Project so that typical folders or locations can be set for individual clients/locations/sites irrespective of when the Project is next opened.