I have read umpteen posts about how PF is a liar generating multiple stories. Without victim-bashing, the George Costanza operator appears to have been KB (keeping her worlds separate).
CB seems nice and truthful, but it is KB who fed her the story about the fiance, engagement, having Thanksgiving with PF and baby, looking for a Chrisymas tree plans - none of which is panning out to be the truth. Sorry, but the neighbor says PF drives to KB's townhome to dropoff and pickup baby, and nothing else. Is the neighbor who lives there lying about what she sees, or was it KB telling tales to CB who prefers the fantasy?
Once the imaginary Thanksgiving eating out with PF, KB and baby is eliminated as just a fiction, we are left with a neighbor who saw PF's truck in front of KB's townhome between 12:30-1:00pm on Thanksgiving, with PF likely picking up the baby leaving KB on her own. Then KB disappears with her phone, keys and purse.
If PF and KB are just coparenting, then why would KB have Thanksgiving with PF and his family? She would have her own plans.
I am not saying that KB did not go with PF or denying that PF could have something to do with KB being missing. I just think there are other plausible scenarios.