I have never run the Calculate Field geoprocessing tool directly against a branch versioned feature service URL, but I believe you are correct in that it will run on the DEFAULT version if you have permissions to do so.
Have you tried unchecking the "Make newly added layers visible by default" option in ArcGIS Pro?
I have that unchecked because several layers I add to ArcGIS Pro are large and slow things down. With that option unchecked, I can add a large layer and configure it (scale visibility, etc) before I turn the layer on or just leave it off.
As far as I know, the only way to run a calculation on a specific branch version in ArcGIS Pro is to add a layer to the map, set the version from the Data Source tab in the Contents pane, and then add the layer to the Calculate Field tool as the Input Table parameter.
"Not all those who wander are lost" ~ Tolkien