OS slows down when I connect external monitor
Kernel task exists to slow things down when the system gets hot. Have you ruled out a temperature rise when running more pixels adds GPU and CPU load? Especially if you run closed clamshell mode. 


https://support.apple.com/en-us/HT207359
Why is kernel_task using so much CPU?
What exactly does kernel_task do?
rMBP kernel_task spikes when connecting more than one external monitor


I would expect your Catalina activity monitor to show a GPU tab but maybe that’s only on some hardware. I also would be sure you’re running the latest EFI and firmware and reinstall the OS from recovery on top of your system. Check system information and build which are circled in red.