Yeah, then it is definetly connected to the cpu, not gpu. (I asume you already set windows +p to duplicate/extend screen once connected and you are connecting to HDMI OUT, not IN)
I would run the following tests:
1. Confirm the drivers are fully up to date (no yellow triangles around or missing the following): Device Manager/Display adapters/ Intel UHD 630 and also the Intel/NVIDIA Audio/Displays ones
2. If not working after update, try disable manually and enable again after few seconds.
3. if that doesnt work, verify in BIOS iGPU /Intel graphics are enabled
4. If you did the inf manual install of any related drivers, ensure to disable windows updates for those specific drivers, restart the laptop on “Driver Signature Enforcement Disabled mode”, reinstall drivers, and try it in this mode.
5. if not working, Try to change back to the old cpu (to test if HDMI works properly)
6. Last resort, Ubuntu usb...
7. if not working, an alternative work around would be a miracast monitor connected through WIFI....
UPDATE: I have been also checking and this would go beyond uncharted waters on a laptop, but there is another method. It would be to get a LVDS to lvds (connect laptop screen) and hdmi extention (connect external screen), there is 5v and 12v, if you get the 5V you could power it via usb 2.0. It should definetly work, then get a software to separate virtually both screens.(around 20 usd)