Google Contacts have started rolling out a feature with its Pay service. The updated Contacts app v2.5 carries contains as a new Send option for making payments. The UI itself is basically the same as the one found in Android Messages.
The user can't use this feature as Send is not functioning properly yet. The rollout seems to be in the very initial phases at the moment, but that should change sooner than later. If you use Google Pay for money transfers at this initial stage, this should definitely come in handy.