Attribute rules for ArcGIS Pro are being marketed as a replacement for Attribute Assistant but lack the same functionality when it comes to manually running rules. There are all sorts of hacks and work-arounds for running a rule manually or running it manually on selected features, but it should only take adding a checkbox in on the preferences when creating an attribute rule for 'Run on Manual' and a button on the top ribbon for running it.
The official ESRI solution, as outlined to me by an ESRI representative at the Southeast User Conference, is to copy the arcade code and paste it into a field calculation for the records you wish to run it on. This is unnecessarily difficult compared to Attribute Assistant. This solution could also be implemented without the loss of functionality for attribute rules as a whole.