Can I filter clients by whether they've sent their records, and bulk-email the rest?

There's no "records received" filter on the client list, so this isn't currently possible directly.

Job status filtering, including grouping by status on the Kanban view, is only available from the Jobs screen and can't be combined with bulk client email from there. This has been logged as a feature request.

You can still bulk-activate a service for a group of clients using Clients > Bulk Actions.