White dots on ASUS Laptop when using HDMI output

Hmm ... The pointed Lines are crooked, interesting. And You don't have a Wallpaper.

  • Are Secure Boot and Fast Boot in BIOS disabled?
  • If Windows is still installed: Is Fast Start-Up in Windows disabled?
  • Did You tried Zorin in Live Mode before You haveinstalled it? If yes: did You had the same there?
  • Did You tried switching from Wayland to X11?

Maybe a Reinstall of the Desktop helps. Try in the Terminal:

sudo apt reinstall zorin-os-desktop

Another Point could be Your Processor/Graphics Unit. Maybe a newer Kernel offers better Support. If You are open to try it with a newer Kernel, here are Instructions: