@Raimondi The new insulation is unfaced stone wool, so it required a vapor barrier on the warm side

Is there a vapor barrier in the rest of the house?

@Julie Praus I live in a cold region and it seems to be on every exterior wall. The same contractor seems to have correctly insulated with the barrier in our bathroom so I'm guessing he simply forgot to install it in the kitchen

For the rest of the house (except the bathroom) the barrier is integrated on the insulation similar to this:

@Julie Praus Hmm I see what you mean. It's a brick house, pretty old, varying climate. I placed a thermometer in that area and it's reading 54% humidity at the moment.

Maybe I should call an insulation contractor or someone knowledgeable in these things for a consultation on that. I guess my contractor would probably argue that it's not needed since he'd be the one that has to carry the repairs.

There's nothing inherently wrong with fiberglass batt-type insulation. The OP notes they are in a "cold" climate zone, so a wall assembly would need either a class I or class II vapor retarder on the interior side of insulation, depending on how extreme the climate is. A good drywall primer and a couple of coats of paint would function the same as a class II vapor retarder although it may not meet prescriptive code requirements in the OP's locale. I wouldn't rip out the cabinets and re-do the construction of a 4' x 8' area.

I agree with Charles Ross Homes. It’s important to try to keep wall cavities dry but it’s more important that they can dry out. With an old house, you most likely have enough other areas of air leakage that your house is adequately drying. I would not worry about this small area lacking a dedicated vapor barrier.

@Wacky Tacky Stone wool / fiberglass batts + warm side vapor barrier seem pretty standard in my area, though I agree that spray foam would have prevented the issue.

@Charles Ross Homes Good idea, I'll make sure to apply a good primer before he installs the backsplash, though for the upper cabs it's going to be tough to get it underneath.

Since the lower cabs aren't installed yet, maybe the bottom 4-5 feet of drywall could be cut out and refitted?

I wouldn't do any surgery on your home given that a couple of coats of paint function as a class II vapor retarder. It's reasonable to ask your contractor to paint behind the base cabinets before installing them.

@Charles Ross Homes Agreed I'd like to avoid having that done if possible.

Perhaps I could have it looked at to confirm it wouldn't cause problems later on, I'm thinking maybe an insulation specialist.

Would you have any recommendations as to the type of professional for a consultation of that nature?

There are a couple of insulation contractors in my area who have a good knowledge of building science. Check around and see if you can find one in your area who is. You could also consult with a HERS (Home Energy Rating System) rater.