Implement simple homeserver users activity statistics (outgoing event count per hour/day)

This issue has been migrated from [#6007](https://github.com/matrix-org/synapse/issues/6007).

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On our public ru-matrix.org homeserver "Glowers club" spammers goes to register new accounts, when I block manually affected account, they register new. So I searching the way to automate detection of spamming accounts, via some metrics, for example - outgoing event count per hour/day.

At now all events are stored in one large `event_json` sql table, but this have no separate indexed field for event author (user_id), so filtering user-owned events from whole table will be too expensive. And I can't see some other table, where can I get events, filtered by mxid.

Maybe some other Synapse tables exists, in which I can simply do something like `SELECT COUNT(event_id) FROM xxx WHERE timestamp > 12345 AND server = 'myhomeserver.org' GROUP BY user_id`?

Or maybe already exists some Synapse module, that will fill `users_stat` sql table with right info (now it have 0 records)?

If not, can you implement some easy-to-use statistic reports of homeserver users, for quickly detecting too active ~spammers~ users for automate alarming and blocking?