Sanity check the `review_recent_signups` script in CI

This issue has been migrated from [#11193](https://github.com/matrix-org/synapse/issues/11193).

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This is a regression that we missed. #11191 spotted it.

I think something similar to `test_synapse_port_db` would do the trick, i.e. a script that a) updates the sqlite DB stored in .ci and b) runs the recent signups script and checks there are no errors.

Could go further and try to actually interrogate the script's output, rather than just checking return code nonzero.

Start by comparing the CI setup for test_synapse_port_db with the .ci SQLite database and the review_recent_signups script. Run the existing CI test and script to reproduce the regression. Done means the database is updated, the script runs without errors, and its output is checked if feasible.

Written by the indexing model from the issue text.