When we finish processing a request, log the number of events we fetched from
the database to handle it.
[I'm trying to figure out which requests are responsible for large amounts of
event cache churn. It may turn out to be more helpful to add counts to the
prometheus per-request/block metrics, but that is an extension to this code
anyway.]
While I was going through uses of preserve_fn for other PRs, I converted places
which only use the wrapped function once to use run_in_background, to avoid
creating the function object.
