feat(sink): dogfood publish-through + docs + retry-storm GIF (S6)

[williamdewitt]

Part of #49 (WebhookSink epic). Slice S6. One agent run, samples/** + docs.

Blocked by #68.

Acceptance criteria

• A runnable dogfood: publish events through Caliber.Webhooks (the delivery loop) into the WebhookSink; with fault injection on, show the retry storm + webhook-id dedup on the dashboard.
• A docs page + sink README documenting the sink and the dogfood; capture the retry-storm GIF (or a scripted repro that produces it).
• README leads with the honest niche (local + .NET-native + signature-aware + fault-injecting + embeddable) — never "nothing exists".

Definition of done

• Builds green; tests green; changes confined to samples/** + docs/**.

Design: docs/design/webhook-sink-design.md (seam #2: dogfood, S6).