If a person has a Single Entry Schengen visa, would a visit to those microstates count as having left the Schengen area?

I know that Monaco, San Marino and the Vatican City count as de facto Schengen, but since they 'stop the clock' for the counting of the 90/180 days rule (per this question) for time spent there, I wonder whether they just consider it also an exit of the Schengen area.

The question is concretely about the Vatican, the other states might be of interest for OP with a similar problem.

It would be quite a hassle getting stuck in the Vatican. There's only one hotel there (Residenza Paolo VI), with prices in the €125-€320 range. but again, it would also be a pity to visit Rome and not visit the Vatican.