If I understand well what you are trying to achieve you could use the padding top trick to have a video with the correct aspect ratio.
1 - Instead of using the video component use the video background component
2 - Upload your screen recording as a background video (webflow will take care of the compression for you)
3 - To find your aspect ratio just a bit of math : (height of your video / width of your video) x 100
ex: 16/9 - (9/16)x100 = 56.25
4 - Set the padding top of your video background element to this result in % (ex: padding top 56.25%)
5 - Set the height of your video background element to 0
6 - As what you want is probably a portrait phone don’t adjust the width of the video background element but instead put it in a div (screen wrapper for ex) and set the desired responsive width there.
I added a few screenshots for clarity:
Hopefully this make sens and it is what you are looking for.
The reason behind is that padding top in percentage uses the width of it’s parent to do the maths.
You can read more and go deeper on the subject on MDN, stack overflow or CSS tricks by searching aspect ratio div or padding top trick.