Mail to or from ops@ that didn't match any client's contacts, a learned sender, or a case number, and that the AI couldn't sort on its own (it sends subscriptions to Admin, invoices to Accounts and bulk marketing to junk by itself). Attach it to a client or a case (the sender is remembered), open a new enquiry from it, hand it to Admin or Accounts, or mark it junk.
Business admin that came through ops@: subscriptions, suppliers, insurance, registrations. Pick who owns it, tick it off when it's dealt with.
Money in or out: invoices to pay, remittances, statements, payment questions. Same deal — an owner and a tick.
Emails from clients that need a person: a question, a date, a yes or a no. Each one is already on the client and the case; the line under the subject is the AI's read of what they want. Reply from Gmail for now (drafted replies arrive once the FAQ is answered), then tick it Done.
The last 30 days: mail the sync filed on a client by itself (with where it went), and what people resolved here. Nothing to action; it's the audit trail.