Does the asus bios allow you to have both the nvidia AND INTEL graphics operational at the same time?
Have you updated your ASUS bios?
Why not have both monitors on the nvidia card?
Download, run, and save the results of this utility as a text file:
Then ATTACH the text file (using the paperclip under the toolbar).
W10 2004, W10 May 2020, W10 20H1, W10 19041 - A rose, by any other name, still smells.
Download and run the .EXE version of the installer from here: https://downloadcenter.intel.com/download/29557/Intel-Graphics-Windows-10-DCH-Drivers?product=126790. If this fails, please post a shot of the error message(s) output.