If you're looking to save money, you can use an Xbox or PS controller if you have one laying around. I used one for OpenMW for a long time and it worked really well.
I don't have a recommendation beyond that, though.
+1 on this. Bluetooth technology and connection with xb1/PS5 controller has improved over the last 5 years. I play PC games on my phone when I want to lay down. The holder is like $15 on Amazon or at stores as well.
I use parsec for streaming games from my PC and that's free as well.
+1 for the Xbox controller. I got a telescoping controller for Xmas last year. I used it a bunch but the ergonomics were all wrong and I started getting persistent pains in my left hand. Switched to an Xbox controller I already had and the pain went away almost immediately.
There's the cheap $2 holders, and there're the more expensive ones that can have the phone "float" over the controller, balancing the weight better. I've seen ones with a ball socket too, so you can pivot the phone to portrait, great for DS emulators.