Thinking about the science behind a contrail being so dark when viewed from the side. Looking at the video frame above.
It's hazy. The landscape and background are a long way off. Most of the light reaching the eye is is diffuse haze light, and not reflected light.
This haze light is relatively bright.
The contrail is facing roughly away from the sun (flying about north west), so it self-shadows itself to some degree, but most importantly it's blocking the haze light.
The plane is solid white, and above the contrail, so it's a lot brighter. There is very little haze between the plane and the camera, but many miles of haze behind it.
The polarizing filter on the photo makes this all look way more dramatic than it actually was.
Basically it's kind on an optical illusion. Here's a white plane leaving irrefutable contrails:
Nice blue sky, because there is no haze. But even here look at the brightness of the contrails, and the brightness of the plane.
The difficult thing here the three dimensional volumetric nature of the air, and the way it affects the light.