Considering all this work is open-source, could some third party make a Qualcomm Snapdragon based handheld console, if Valve decides not to make a Steam Deck Mini?

I really loved the idea of the Steam Deck, but I'd prefer to play something that's more like the size of a PSP or a Switch Lite at most.

There's already a ton of Snapdragon based handheld consoles, they're mainly marketed for retro system emulation but you can do whatever you want on them. They usually run Android out of the box though, not plain Linux.