It is weird, but they're old lenses, and there was no such thing as video in a home camera back then. It's probably some limitation in the lens itself. I think I got my 35-70 in 1985 or 86.  The earlier lenses had 5 contacts, and I think later ones had 7. Not sure which version you have, but if it's a 5 contact lens that could be it. Just a guess. 

Yes both lenses are compatible and have full tracking. It’s just weird that in video mode you have to use automatic exposure with auto focus. But if you want manual exposure you need manual focus on. It makes no logical sense.

Ok, but did you check Sony's website for compatibility with that lens? There are some differences between models. For example, the 80-200/2.8 APS HS G has full tracking, while the 500/8 Reflex AF has only stationary center spot.