Still works over the Internet once it is paired since about 2018’s Remote Play Anywhere. I think you don’t even need to open ports in your router anymore (not super sure about it).
Or you can use a rented PC (like Liquidsky, Paperspace and Shadow) if your home internet has to little upstream like so: https://steamcommunity.com/sharedfiles/filedetails/?id=1398383317
Steam really needs to explain it better. I couldn’t find a definite feature or requirements list. The FAQ only mentions that it might work with cellular data:
Can I use the Steam Link app with my cellular network? Using Remote Play Anywhere with your cellular network may work, depending on the policies of your cellular provider.
https://help.steampowered.com/en/faqs/view/7112-CD02-7B57-59F8