If you're in the market for a new device, look at https://openwrt.org/toh/views/toh_available_16128 as a first step (and avoid devices with Broadcom's involvement).
I'd also strongly suggest to have router and access points as separate physical devices.
A great step up for someone with an AIO consumer router/WiFi AP would be to get something like that as a router, flash OpenWRT on the old router and transform it into a "dumb" access point.
It's my favorite OpenWrt router so far, and I've owned quite a few since I started using it on a WRT54G :)
(...Personally I avoid Intel CPUs best I can, though. AMD's ME equivalent on the APU can actually be disabled, which happens to be something I care about for something like router)
All I remember regarding AMD PSP was that one motherboard manufacturer showed the option after an update and the other you had to flash a modified BIOS to expose it.
But besides this discovery by a user, there hadn't been any research or verification that this software option does what it claims.