docs: add proxy mode documentation

- Matrix docs: full Proxy Mode section with architecture diagram,
  step-by-step setup (host + Docker), docker-compose.yml/Dockerfile
  examples, configuration reference, and limitations notes
- API Server docs: add Proxy Mode section explaining the api_server
  serves as the backend for gateway proxy mode
- Environment variables reference: add GATEWAY_PROXY_URL and
  GATEWAY_PROXY_KEY entries

website/docs/user-guide/features/api-server.md

@@ -278,3 +278,9 @@ In Open WebUI, add each as a separate connection. The model dropdown shows `alic
 - **Response storage** — stored responses (for `previous_response_id`) are persisted in SQLite and survive gateway restarts. Max 100 stored responses (LRU eviction).
 - **No file upload** — vision/document analysis via uploaded files is not yet supported through the API.
 - **Model field is cosmetic** — the `model` field in requests is accepted but the actual LLM model used is configured server-side in config.yaml.
+
+## Proxy Mode
+
+The API server also serves as the backend for **gateway proxy mode**. When another Hermes gateway instance is configured with `GATEWAY_PROXY_URL` pointing at this API server, it forwards all messages here instead of running its own agent. This enables split deployments — for example, a Docker container handling Matrix E2EE that relays to a host-side agent.
+
+See [Matrix Proxy Mode](/docs/user-guide/messaging/matrix#proxy-mode-e2ee-on-macos) for the full setup guide.