His resume in "Relics" includes "freighters, cruisers, starships", eleven in total. Supposedly, he ever only worked on two starships (and was Chief Engineer on both, but never on any of the previous ships), unless there were assignments during the movie era that we aren't aware of, or pre-TOS assignments that go unmentioned. But we don't know for sure.
FWIW, no lesser Starfleet vessels are mentioned in the "Relics" list. "Starships" in TOS parlance apparently are the same thing as "heavy cruisers", so the word "cruiser" here is likely to refer to pleasure cruiser instead.