Nope. Only the 6000 series (mobile) and 7000 series (desktop) CPUs/APUs have integrated GPU HW AV1 support.
From AMD GPU Decoder Device Information
and [Reddit r/AV1] List of CPU SOC with AV1 support
The AMD APUs (CPU with integrated GPU) with HW AV1 support are:
- Radeon Graphics (Rembrandt/Raphael/Mendocino)
- Radeon 610M
- Radeon 780M
This is how AMD defines AV1 support from the GPU graphics technology viewpoint:
- RDNA2 = AV1 decode (RX 6800 GPUs)
- RDNA3 = AV1 decode/encode (RX 7900 GPUs)
Here is how that maps from the GPU to the AMD APU Radeon iGPU features:
Source: AMD Reveals Mendocino Zen 2 APUs With RDNA 2 Graphics | Tom's Hardware
-
Rembrandt = Ryzen 6000 “premium” mobile CPUs = Zen3+ with RDNA2 = AV1 decode only
-
Mendocino = Ryzen 6020 “budget” mobile CPUs = Zen2 with RDNA2 = AV1 decode only
-
Raphael = Ryzen 7000 desktop CPUs = Zen4 with RDNA3 = AV1 decode and encode
Your APU, the Ryzen 7 5800H is a mobile CPU (Cezanne) with a Zen3 core with the Vega 8 iGPU technology. Notably, this is not RDNA-based, and as a result, all of your AV1 encoding and decoding are being done by the CPU, and not by the native iGPU. In short, no HW AV1 support. 
Sorry about the news you probably didn’t want to hear.
And yes, AMD’s CPU numbering system is just a hot mess.
Here is the Anandtech secret decoder ring.