Track external requests in stats

When the Prometheus integration in !82 (merged) is merged, it might be useful to extend our stats to track the number of external requests, e.g. to SNS SimilarTerms and AutoClassify API, to figure out how well our caches work. (So we might want to track both cache hits and misses if the overhead is palatable.)

This might also be a good time to reconsider using a single mutex around all the parts of the stats, e.g. incrementing access counts and recording search terms could run in parallel otherwise. And counting request could use atomic integers instead of a more heavy weight synchronization scheme.