Hi, @josch
Nice to see fellow Omen user trying out Garuda.
Regarding you issue, see
Actually, HP Omen are made in such a way that HDMI ports are hardwired with NVIDIA GPU. So only NVIDIA GPU has access to it, as far as I know.
So, you must switch to dedicated GPU to use HDMI ports. I am unsure about Display Port, but I guess it would be hardwired too.
I hope this solves your issue.
Also, I saw some users have been facing issues with Nvidia on Arch Linux in general after recent update. If your issue is still not resolved, report back here, I will have a look tomorrow.
Have a good day.