On three of the four dates the girl said nothing? Red flag.
This is not usual shyness. Effectively, he went on one date with her. And then got engaged.
I would be very concerned about the personality of someone who doesn’t speak on the first three dates. Is she perhaps selectively mute?
Also, it’s great that the parents get along, but that’s like 10% of the shidduch, and that’s being generous. What about the other 90%? Shared goals, attraction, liking the other’s peronality, communication, ability to navigate disagreements…?
It seems like he doesn’t know much about her at all. Why get engaged like that?