As others have mentioned they are custom parts, but if you were forced to qualify them as either "laptop" or "desktop" parts they are much, much closer to AMD's laptop lineup than the desktop ones. Monolithic design with integrated GPU is not what AMD's desktop lineup has looked like.
One thing thats under-appreciated is the immense design/tape out cost (9 figures these days, maybe more?) of a fully custom chip. That is a huge flat expense, hence one does not simply make a custom design unless the volume (or margin) is absolutely enormous.
AMD/Nvidia/Intel can't just casually crank out an APU for Valve, as one might think. I'm not even sure MS/Sony can justify a die shrink this generation... Heck, maybe the PS6 will run commodity PC hardware.
Compared to what came before, the previous (Modified AMD Jaguar APUs) and the current-generation (Modified AMD Zen 2 APUs) consoles are commodity PC hardware compared to whatever bespoke cost-optimized ISAs consoles used to be built around. So in a way, it's already somewhat commodity PC hardware under very heavy TPM lockdown.
They have been there pretty consistently, for example they’ve been the SoC provider for a few generations of Xbox and PlayStation consoles, now.