There are many devices that can do this that are cheaper than a Steam Deck and have great screens and controls. They come in all shapes and sizes.

I'll recommend Retro Game Corps as a great gateway into this scene: https://www.youtube.com/c/retrogamecorps

If you just want a huge list of what's available: https://docs.google.com/spreadsheets/d/1irg60f9qsZOkhp0cwOU7...

I'll plug my own channel as well as I own many of these devices: https://www.youtube.com/@forthenext