CP contract definitely isn't an easter egg and it isn't rare. it appeared to me as first ever available contract. and I did nothing specific. I believe that plot or actions ha no impact on what contract would be available, that it's for a false-random numbers to decide.
I'm curious. Volksauto seems to be the pinnacle of all partners, it's locked from the start. I imagined they can give some rare parts as a reward. you mentioned that you had Volksauto available, have you ever did it? what they offered, just more money?
also have you ever reached the top list of Twitch streamers? I guess you could have since you've seen Volksauto