Gas Water Heater Vent question

Hi all-

I’m still new to this business so there are things I haven’t seen yet.

This is the gas vent from a water heater in the garage. I thought the ceiling damage was due to moisture intrusion but I can’t find an active leak or staining. Would this be caused by the vent not having any gap between it and the drywall ceiling?

Thanks!

Heat

Thank you!