Personally my inclination would be building a PC. There are just too many small things here that make a PC seem a better fit in my mind
A PC can be upgraded over time. A PC can run Windows, and from what I understand there’s still some willingness to tinker and adjust stuff needed to get stuff working on steamdeck at times (I say this as an exclusively linux user for the past like 10 years, though I don’t have a steam deck and haven’t played with gaming on Linux). And ultimately the main selling point of the deck sounds like it would be pretty secondary for you
I’d love to tell you go with the cheaper option, but I think long term the PC just makes more sense. Even if you just wanna run linux and use a distro that replicates the steam deck’s configuration and setup, the PC will trade the portability you don’t seem particularly interested in for upgradability that I think is really worth it. If you’re looking to save money my gut says you’d be better served by getting used components, a used case, and a good power supply you can upgrade around.
Thats my 2c as someone fairly unqualified to give advice lol. Regardless, I hope you find the right path for you!
But I think the big consideration is whether to trade portability for upgradability, or vice versa.