I found the solution for my hardware 
— the problem was simply not reading the manual.
PCIe2.0 M.2 dual Hat supports PCIe Gen 2, and PCIe3.0 M.2 dual Hat supports PCIe Gen 2 and PCIe 3.
Step 1: Enter the following command to open the /boot/firmware/config.txt file
sudo nano /boot/firmware/config.txt
Step 2:Add the following to the [all] section at the end of the /boot/firmware/config.txt file:
dtparam=pciex1
dtparam=pciex1_gen=3
dtoverlay=pciex1-compat-pi5,no-mip,mmio-hi
The Hailo-8 accelerator is now working in Home Assistant OS on a Raspberry Pi 5 with the ASMedia ASM2806.
