

The key problem why “Runs on SteamDeck” exists is not the raw power of the SteamDeck (or lack thereof) but the compatibility with Linux. Unless someone decides to utterly cripple a handheld for the sake of battery efficiency any game labeled with SteamDeck support will also run on any other handheld running SteamOS.
The problem with the SteamMachines ultimately was the lack of game support. The hardware confusion was just the cherry on top. You could even argue that the lack of supported games back then meant a limited number of customers would be interested which in turn led to companies releasing underpowered hardware. By that logic one can even claim the failure of SteamMachines is entirely down to the piss poor Linux support then.
The 14th gen didn’t only have problems with Linux and I still don’t trust Intel when they say they “fixed” the CPUs disassembling themselves. Given the money involved I’d definitely advise against 13th and 14th gen Intel in any case, just not worth the potential headache down the road. Either go with older Intel or AMD.