No camera movement when capturing video

Is there a reason you’re using 4.26? That is quite old by UE standards, and not really “supported”. 4.27 should have all the best qualities that you’d want from UE4 if there’s a reason you can’t upgrade to UE 5.3 (which I also recommend in 99% of cases)

MRQ was introduced in 4.26, but it’s a pretty early version. As of today, that’s the official way to render any content from sequencer.
If you are rendering a sequence that has a camera cut track (not just nested shots), I would expect the camera piloting to work. This is a little weird and there must be some little quirk somewhere. Make sure you try rendering the same sequence in a completely new template level to make sure nothing in your level is messing with it.