No patching nothing but spray painting?

If the pets wreck the carpet, no harm no foul.Get a pro to take the cabinet doors off, sand, and spray them in a booth with oil based paint and reinstall with new hardware.

A silicone caulk, some type of expandable spray foam, or mortar?

Painting is typically in the $1 per sf for 2 coats for rolled, spray is a little cheaper (RS Means).Rough#  733 sf clng, 880 for inside of ext walls (assume 25' x 30' at 8' = 880 sf). 

But he basically used a spray foam dispenser to areas which had largergaps and used a special sealant to seal it.

We sprayed 2 or 3 coats of high quality undercoater and 2 coats of SW ultra classic.

You don't know what product they used before - oil based vs water based, etc......you don't want the trim peeling in a year.....If you can afford a little extra $$, have your painter spray the cabinets with enamel.

I personally specialize in interior banister installation and spray stain finishing.

Oh and some sort of cooking spray.

You can skim coat and then spray texture the area to blend in.