You can use Steam Link to stream games from your PC to your phone or tablet.

For decent handheld controls, simply pair a PS4 or PS5 controller (or even an Xbox Series X controller) with your phone/tablet over bluetooth.

All you need now is a phone mount for the controller and you are set. For example, google: "PS5 controller phone mount" for a big selection of options available for sale.

The only downside to this type of gaming is the latency. Some people don't mind the latency from streaming games, but it really bothers me.

Given steam PCs can stream between each other, I suspect this would be able to as well. Otherwise there's the nvidia shield portable, though I haven't tried it.

This can do that. Or you could get a clamp controller for your phone, and use the Steam Link app.