I use a product named Edius, from GrassValley.
It's a real-time non-linear editor, expensive though, but is used by television studios. The workflow is very similar to a DAW, but of course allows chroma-keying, video adjustments, green-screen, effects and much more.

I also use Camtasia from Techsmith which could probably deliver something quite well, but maybe rendering to mp4, mpv etc would be required to get the final output (single track vision would play real time off the timeline, but multiple PIP would require rendering first). They have a free trial. It's much cheaper than Edius, but still not as cheap as others.

BIAB & RB2024 Win.(Audiophile), Sonar Platinum, Cakewalk by Bandlab, Izotope Prod.Bundle, Roland RD-1000, Synthogy Ivory, Kontakt, Focusrite 18i20, KetronSD2, NS40M Monitors, Pioneer Active Monitors, AKG K271 Studio H'phones