The bios seems to define 4 outputs, one hdmi on the nvidia, one hdmi and two displayports on the intel gpu. All show ‘disconnected’. What kind of connectors does your notebook actually have? Which did you try?
There is a single physical HDMI port. I have tried this with a straight HDMI-HDMI cable, an HDMI-DP adapter, and have also tried with a dual-HDMI port USB-C hub; none of these things worked on two different monitors. What DOES work is a straight usbC-DP cable.
According to the logs, your external hdmi monitor is connected to the intel igpu, not the nvidia. Please check the monitor manager in gnome control center to enable it.
The HDMI port does not work using Windows either. However, HDMI ports on a USB-C hub also do not work, so I’m disinclined to believe it’s the HDMI port itself. However, since it’s present on both Windows and Ubuntu, I’m guessing a BIOS problem.