I needed to google the laptop model and the Nvidia GPU card that you mentioned it has installed.

I saw the specs that it uses a Ryzen 7 6800H APU processor with various Nvidia RTX 3050/3060/3070 GPU cards: https://www.asus.com/laptops/for-gaming/tuf-gaming/asus-tuf-gaming-a17-2022/techspec/

Under the laptop various models they all seem to have the same Graphics driver for Nvidia but none for the AMD APU Integrated Graphics: https://www.asus.com/laptops/for-gaming/tuf-gaming/asus-tuf-gaming-a17-2022/helpdesk_download/

I would download the Nvidia Graphics driver and Nvidia Control Panel and install that so that your RTX3060 will be enabled. In Device Manager under "Display" it should show two GPUs, AMD IGPU and Nvidia DGPU.

But it seems like Asus only has a AMD CONTROL PANEL but doesn't install a AMD Driver for the APU's Integrated Graphics. But does install a Nvida Graphics driver for your RTX3060.

It seems like if you install both AMD and Nvidia Graphics drivers in the same laptop there will be a conflict between each of the drivers. Maybe that is why the laptop driver download page only has a AMD Control Panel to install and not any AMD Graphics driver but only Nvidia Graphics driver for your more powerful RTX3060 DGPU card.

So I would use DDU to remove all AMD Driver and Control panel first and then download Asus OEM AMD CONTROL PANEL and install that.

Then I would use DDU again to remove any Nvidia driver and Control Panel and then download and install Asus OEM Nvidia Control Panel and Graphics Driver.

Afterwards I would go back to Device Manager and make sure under "Display" your Nvidia GPU is showing without any errors. Also it might show the AMD IGPU which Device Manager might have installed just the driver by itself.

If both are showing and there are no errors in Device Manager now see if you can hook up 2 Monitors without issue.

Some laptops does have a limit to how many Displays it can connect to. Generally 2 displays is the minimum for most laptops.

EDIT: Here is AMD APU Integrated Graphics driver from AMD Download page: https://www.amd.com/en/support/apu/amd-ryzen-processors/amd-ryzen-7-mobile-processors-radeon-graphic...

But I wouldn't install this driver because it might cause a conflict with your Nvidia Graphic driver. IF you do try to install it make sure to either make a Windows Restore point or better yet do a Windows System Backup in case your laptop is messed up.

If it is messed up and it won't boot into Windows restart the Laptop 3 times in a row before Windows loads up and it should go to automatic Windows Repair mode and then to Windows Troubleshoot Menu where you can click repair Windows Startup.