Feature or enhancement

Run the tests on an --enable-pystats build as part of CI and/or buildbots.

Pitch

In #99701, it was discovered that the --enable-pystats build was broken by an unrelated change. No harm in that -- it's the usual unexpected interaction that happens all the time.

But if we want --enable-pystats to continue to work, we probably need to have some CI for it.

I don't feel super strongly about this -- every new bit of CI has a non-zero maintenance cost, and in this case there is a really small audience for collecting these sorts of stats (mainly those working on the specializing interpreter).

However, if there is enough interest, I did want to suggest it and offer my time to put it together.