Currently `UnifiedStatsReporter::flushTracesAndProfiles`
can kick off requests when computing the source
ranges for collected entities, which will try to
record additional stats about the requests.
This currently happens to work without issue,
but #29289 bumped the counters down slightly such
that the vector storing the stats now performs a
re-allocation when we do a reentrant stat entry.
This then caused a use-after-free as we try to
continue iterating over the old buffer.
Fix this issue by refusing to record any new stats
while we're flushing out the ones we've already
recorded.
fe906574cd