A linear polariser won't solve the 'angle' problem either. It has nothing to do with the type of filter, as has already been stated.
That's correct. The only angle that makes a difference is the angle of view relative to the sun, which has the maximum of blue skye polarization at 90 degrees from the direct sun angle.
Fike, since all polarisers have to be rotated for maximum effect based on polarisation of reflected light coming into the lens, it would do no good to put a polarising type of coating on thefront element because it ould not always have optimal effect.
It is indeed unlikely that a polarizer would be somehow built in, it even doesn't make sense if it can't be manually rotated.
It is possible that your two fisheye lenses have different types of anti-glare or similar coatings due to the extremely wide angle the lens is taking in and these types of lens coatings can impact contrast and colour.
I think it is more likely that the extreme angle of view triggers the light meter to reduce exposure (because it picks-up a lot of lightsources). That reduced exposure would be rendered as a darker, more saturated, sky.