I have a hybrid nvidia and intel, when I connect via hdmi it switches on the nvidia driver and uses the intel on my laptop. Seems to me that you may want to have nvidia drivers installed so that one screens uses the nvidia and the other the amd gpu. Else the hdmi will appear black.
I have absolutely no experience with AMD. Maybe you need to install the correct driver for that gpu? Nvidia seems ok with 460x. As I recall amd maybe integrated in the kernel.
I would check whether this amd gpu is supported by your current kernel or needs a newer or perhaps older lts.
Edit: manjaro has a easy gui tool to try/install another kernel. Needs a reboot after install though. I also like to mention that I often saw problems on linux forum with HP and their dual gpu, something with the vendor bios that makes our life a bit more difficult on linux…
Edit2: saw that you posted on this thread
Did you try install the dual gpu driver as mentioned there via terminal?