While the external display is connected, check NVIDIA Control Panel’s multi-display section to see which display outputs (including the one for the built-in display) are physically wired to which GPU. It’s possible that the HDMI and/or USB-C outputs are wired to the NVIDIA GPU while the built-in display is wired to the Intel GPU. In the latter scenario, the NVIDIA GPU when needed should be acting as a render-only device that passes completed video frames to the Intel GPU for output to the display. In many laptops with dual GPUs, all outputs are wired to the Intel GPU for battery life reasons, because when outputs are wired to the NVIDIA GPU, then it has to be on whenever a display is attached, even if nothing graphics-intensive is going on. However, some applications don’t work as well under this “NVIDIA Optimus” setup as they do when the NVIDIA GPU directly controls the display output in use. If you find that this GPU wiring difference exists on your system, I’d recommend reaching out to the software vendor asking if they have any suggestions for how to get the expected performance under an NVIDIA Optimus setup.

The only systems I’m aware of that give direct control of the BUILT-IN display to the discrete GPU are a) systems that lack or completely ignore the Intel GPU that’s normally built into the CPU, and b) systems that have BIOS options that allow you to choose which GPU controls which outputs. I don’t know how many laptops in the former category exist anymore, since that design comes with a battery life penalty, and even gaming/workstation laptops are expected to have decent battery life these days. In the latter category, I know the Precision 7x20 and newer models offer this capability, which they can do because they have a more complex and expensive motherboard design where all display outputs are wired to essentially a switcher, and the switcher is wired to BOTH GPUs, allowing the user to choose which GPU should have control.