Though unfortunately the Mini-ITX space has been left do dangle for a few years now; most of the affordable (<300 money) boards have pretty old CPUs.
AMD hasn't had something new in that space for a very long time - E-350/450 based boards were just recently discontinued, and that was a 10 year old part. The only other boards still available seem to be re-spins to sell of 5-6 year old APUs. These were decent in their time, but time has moved on. The E-350/450 were also bundled with crappy southbridges which consumed way more power than the CPU itself - when you see one of these boards, the smaller, fanless heatsink is for the CPU, the big one for the southbridge.
VIA has been gone for some time.
All the Intel boards are 14nm or 22nm parts, usually from 2014-2017. Newest boards seem to use the J4125 - a Goldmont refresh from 2019.
Intel at least offers some newer stuff in the NUC form factor (though at much higher prices as well). NUCs are pretty non-standard form factor though and offer PCIe only through M.2, so for I/O you'll need an awkward M.2-to-PCIe adapter with a cable. AMD really only has that 4700S kit (which uses a PS5 SoC with defective iGPU as I understand it) at around 400 currency. The 4700S seems to have ridiculous idle power draw (~80 W - maybe power management for the GDDR and other parts are disabled together with the iGPU).
There are some ARM boards now with PCIe. The RPi CM4 has a PCIe 2.0 x1, which is not a lot but maybe good enough for some use cases. The RockPro64 has an PCIe 1.0 x4 slot; the RockPi4 has an extremely awkwardly positioned M.2 slot (same PCIe 1.0 x4, it's the same SoC as the RockPro64).
None of these are great options.