Can an External Monitor improve GPU performance for video editing?

External monitors only increase performance if you are using an external graphics processing unit (eGPU), and even then they only save a few ms per frame rendered.

If you need more performance you will either need a new/newer computer or an eGPU. eGPUs are not compatible with Apple Silicon going forward so it may be better to invest in a new computer rather than dumping $250-500 into an eGPU.

The MacBook Pro (13-inch, 2019, Two Thunderbolt 3 ports) has an Intel integrated GPU (Iris Plus Graphics 645), and no discrete GPU. If you add an external monitor, you're just going to increase the load on the CPU and GPU. Instead of making the GPU run faster, you'll be forcing it to spend its time on refreshing two displays.

This Mac came with 8 or 16 GB of storage. Video editing tends to make heavy demands on RAM and storage, so if you are doing heavy video editing with a machine with only 8 GB of RAM, that could be part of the problem. Before you ask, RAM on this machine is soldered in and non-expandable.

<<. I think MacBook are not the best for video editing in general. >>

No that is not correct as written. Your 13-In MacBook Pro is not very good for Video editing because it has a "compromise" GPU built into the processor that is "just OK", NOT what you would want for Video Editing on a daily basis.

The 15-in MacBook Pro from the same year is a perfectly adequate Video editor, not because of the screen size but because the higher spec 15-in models have an additional discrete GPU that is much more capable.

Attaching an external GPU to an underpowered MacBook Pro 13-in is not a good move for the future. that money would be better spent on a more capable Mac.

Apple-silicon Macs with at least the Apple-Silicon PRO processor are very good video editors. This includes the MacBook Pro with PRO processor. But if you do not demand portability, you pay dearly for light weight, battery-capable and the lovely built-in display. The same money will buy More capabilities in a desktop Mac.