Hm, what does the following show?

cat /sys/bus/pci/devices/0000:02:00.0/power/control               # GPU
cat /sys/bus/pci/devices/0000:02:00.0/power/runtime_status        # GPU
cat /sys/bus/pci/devices/0000:02:00.0/power/runtime_usage         # GPU
cat /sys/bus/pci/devices/0000:02:00.0/power/runtime_active_kids   # GPU
cat /sys/bus/pci/devices/0000:02:00.1/power/control               # HDA
cat /sys/bus/pci/devices/0000:02:00.1/power/runtime_status        # HDA
cat /sys/bus/pci/devices/0000:02:00.1/power/runtime_usage         # HDA
cat /sys/bus/pci/devices/0000:02:00.1/power/runtime_active_kids   # HDA

I can't see anything in dmesg that the HDA controller is bound to a driver.
What does the following show?

ls -l /sys/bus/pci/devices/0000:02:00.1/driver