I conclude that Venmo and PayPal do indeed share contact info. We're only two data points, but given the near-identical situation, this seems very likely. Lag time between joining Venmo and getting that same email alert myself, was only one day. For you it was three. But other than that, they are precisely the same sequence of events. Thus, looks likely the reason we each got that alert email ("You added your phone number to your account") was the fact that we each had just joined Venmo after having had PayPal accounts already without phone number associated.
