This came out here a few times with different titles.
I have a layer in Pro with open attribute table.
When I use calculate field tool or when I write a line in the python windows to update any values the attribute table is refreshed automatically and show the new values.
More then that, when I run a python within a tool that have only the layer name in the toc Pro will refresh the table.
When I have the full path of the data in my update script the table is not refreshed.
This is fine since Pro should not check all the time if the source data is updated.
What can be a big help is a button "Reload data".
Pro uses many caches and I could not fine any way to see the updated data other then remove the layer from Pro and bring it back or just close the project and reopen if I do not want to lose symbology.
The same is true if the source data was update in any other way (csv on disk or sql update in database)
Thanks