With the release of Pro 2.4 within 2 months where you can publish directly from Pro to ArcGIS Server with a GUI, it would be great if this tool, that is part of ArcMap/ArcCatalog, can be added to Pro.
I guess a workaround where you are keeping ArcMap around, is to perform this function in ArcMap and then import the mxd into Pro and then publish that aprx. It's a pretty hacky solution without a comparable Set Data Source tool in Pro which has existed in ArcMap for many, many years.