The AM5 chips come default with a small 2CU iGPU on the IO die. Its not a very impressive iGPU - literally the smallest AMD can provide with the RDNA2 architecture, since RDNA2 CUs come in pairs - but it is sufficient for normal desktop use. I am using an R7 7800X3D's iGPU in one of my servers for display output when I need to access it.
The 7800x has a iGPU, but its not an APU, and the Zen 4 7000 series is the first one with iGPU?
Are there any Zen4 APUs with Socket AM5 available or in the pipeline? Zen4 is a must, otherwise no AVX-512.
Yes, the Zen4 7000 series is the first one where the normal CPUs have iGPUs (except for some specific SKUs equivalent to Intel's F-series). Functionally this makes them APUs in AMD's parlance, but they are not marketed as such, since normally for desktop platforms, AMD only markets laptops chips converted to desktop sockets as APUs due to their larger iGPUs.
If you specifically need both zen4 and a large iGPU, you may have to wait a while for AMD to release one, but if you are ok with the small iGPU, any of the existing normal or X3D Ryzen 7000 AM5 zen4 chips should fit your needs.