What works, per provider.

Gmail — folders vs labels: Gmail uses a flat label system rather than hierarchical folders. "Move" is implemented as label add/remove. Native copy is not available via the Gmail REST API.

Permanent delete: Gmail moves to Trash when you delete — permanent expunge is not exposed by their APIs. IMAP providers (Fastmail, iCloud, Yahoo, Zoho, Yandex, Generic) support both trash and hard expunge.

Contact search (live scan): All providers support contact_search, which finds matching correspondents with a live, header-only scan of a recent window of your matching mail. There is no contacts table — nothing is stored between calls, and counts reflect only matched messages in the scanned window.

Scheduling: Supported for all providers via a server-side scheduled_sends queue. Use the schedule tool's create, list, and cancel actions. Delivery uses each provider's existing send path — no provider-native scheduling API is required.

Signatures: A per-inbox signature is appended server-side on every send, reply, forward, draft, and scheduled message — this works on all providers. Signatures support rich HTML formatting (bold, italic, headings, lists, colors, alignment, links) and a hosted logo/image; set them in the dashboard rich editor or via the signature MCP tool (which accepts signature_html). Images are referenced as hosted https URLs and render across every provider, though some clients (e.g. Gmail) may hide them until the recipient clicks "display images" — that is normal for any hosted-image signature. Use signature_reply_mode to control whether the signature appears on replies and forwards. Per call, pass include_signature: false on email_compose or draft to skip it.