You could go for the 8600G/8700G APUs without a graphics card. This should give you better performance than the Steam Deck and the option to later add a graphics card.
I’ve added a screenshot of a german shop that sells these for 649€ without operating system:
I did not find any pre-built PCs with this CPU, that’s why I’m referring to this shop that does the assembly for the customer.
Prompt: gollum from lord of the rings, wearing a colorful suite, no tie, full body image (Bing Image creator)