How can I re-add a route analysis feature layer from catalog back to a map (in arcgis pro) if it gets removed? I understand the feature dataset is within the geodatabase. Is there a way to re-add this feature dataset so it's back in the project as if it was when I originally created it (grouped, symbolized, ect)?
You cannot. If you want to re-add the layer in the future, first use the Save To Layer File tool to save it as a .lyrx file, or save it as a layer package. If you have not done either of those things, there is no way to retrieve the layer from its feature dataset. It's gone.