OP, Forget the 'if you can't trust your partner you shouldn't be in a realtionship' brigade.
Thats trotted out each and every time someone posts about something that doesn't make sense to them. Shortly followed by those in 'healthy relationships' that wouldn't dare think to question their partner about anything even if they were caught with their pants down in the middle of an orgy.
As far as i'm concerned a healthy relationship is not about blindly trusting another person. of course you trust them, until something makes you question something. I mean what idiot would go through life thinking no one would every betray their trust, ever? Oh yeah - those in 'healthy' relationships who never question a thing even if it was poking them in the face.
Anyway, when a partner does something out of the norm, when theres a distinct change in pattern around something and then you discover they may well have been doing something they say they haven't, any normal person is going to go, whoa, hold on a sec.
In your shoes OP, I would not say anything at the moment about the deleted chats. Maybe just bring up something about when did your meeting end on my bday - you didn't call, just casually, and see what he says he was doing instead of calling. I think that would answer alot of it for you.
And when someone does something that makes you pay attention, don't think its wrong at all to try and work out whats going on. Don't let this eat you up though as could be totally innocent. May have been deleted by accident, it does happen. I'd certainly though keep an eye out though to see if anythijng else doesn't make sense in the coming days/weeks.
How well do you know things about her? Any chance you could ask him to message her with a question/advice for something for you? I don't know if shes into a certain hobby, it wouldn't be odd for a work collegue to message and say their partner interested in said hobby and could they recommend xyz?
And then see if that thread gets deleted? or just left with no further or just normal work communication between them.