They kind of did. Check the application menu, and at the bottom of it you’ll find the lost and found category. Now you can right click on the nested desktop entry and click add to steam.

Sunshine and moonlight are really good streaming solutions, but afaik they are based on local network. If you want to stream over the internet, just like other comments mentioned here, use RealVNC or anydesk. The quality will be dependent on your internet speed.

Currently I’m using Sunshine on the steam deck and moonlight on the PC. To turn the screen of the deck off I’m using a dummy plug. Works well.