Your mailboxes, as Claude connectors.
Create a connector for each mailbox, decide exactly what Claude may do with it, and add it to Claude as a custom connector. Every connector has its own address, its own sign-in and its own permissions.
One address per mailbox
Each connector lives at its own URL and Claude signs in to exactly that one.
You set the limits
Switch tools on and off, cap results, allow only certain recipients. Changes apply to the very next call.
Nothing leaves unseen
Sending is off by default and works on drafts you can review. Every call is logged without message content.