I have an HP 17-cp1035cl laptop with IRIS graphics. While I don't use an external monitor, I have plugged in (via HDMI) a projector to watch movies. It works.
Look through my prior posts to see all the hoops I had to jump through to get ZorinOS working on this machine... none the fault of ZorinOS, all due to lazy UEFI programmers.
You'll also see in my prior posts a method of updating the UEFI on your machine (HP generally only provides Windows-specific files except for servers). If you don't have the latest UEFI, try updating it to see if HDMI starts working.
Also in my prior posts... the method of using Ventoy to format the Ventoy USB stick as GPT and putting ZorinOS (and Win10PE) on the Ventoy USB stick. Then you can drop any distro's .ISO file onto the Ventoy USB stick to try it out... but I'd keep ZorinOS (and Win10PE) on there. The Win10PE is for updating your UEFI (and your Elan touchpad firmware, and your SSD firmware (if you've got SSDs)).