The nvidia dGPU uses the iGPU graphics subsystem on optimus laptops for HDMI output. Only on advanced optimus laptops is the output routed directly to the HDMI port when switching to the dGPU.
This works on Windows without any issues, but not on Linux.
At the end of last year, Nvidia announced that it would make changes to the driver (and if I’m not mistaken, to the Linux kernel as well) to improve this.
What happened? No idea…I don’t follow the development of the drivers. Personally, I avoid Nvidia in general.
Since I know your topics and all your issues:
You are not the only one whose HDMI port does not work with the current Nvidia drivers on an (advanced) optimus laptop (with nouveau everything works without issues).
You are also not the only one who generally has Linux issues (such as the problem with the screen brightness) on an HP Omen laptop. Some of the Omen laptop models do not seem to be 100% compatible with Linux.
We generally do not recommend solving problems by reinstalling the operating system. But you have now installed and configured so much to solve your problems - and the list of new issues is getting longer and longer.
I would recommend that you make a backup of your data, then boot the garuda-live.iso with the option for open source drivers, reinstall garuda and after installation do NOT install any nvidia drivers but use the open source driver nouveau - to test whether everything works without issues.
We don’t know your use case, but if nouveau is not enough for you, then you will have to install the nvidia drivers and pray.