Synapse doesn't cache keys for remote users that don't have any devices.

This issue has been migrated from [#10151](https://github.com/matrix-org/synapse/issues/10151).

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This can result in requerying the same keys again and again and again. The root cause here is that we check if we have a cached copy of the keys for the user by looking in `device_lists_remote_cache` table, which only gets populated if the remote user has at least one device.

If a client tries and gets the keys for a lot of such users at once, it can hit the failure mode where the request times out, it retries, and Synapse ends up sitting at 100% CPU just refetching the same user repeatedly, without making any progress.