Add persistent agent messaging and shared chat bubbles

Connect Sybil to the Pi root conversation with authenticated REST and WebSocket
APIs, persistent read state, and a dedicated agent tab. Keep optimistic messages
stable through delivery and retries, and animate arrivals without losing the
reader's scroll position.

Share bubble styling with regular chats and remove the obsolete admission sender.
Reject malformed upstream receipts and WebSocket upgrade requests, with regression
coverage and updated API documentation.

Validated with 51 web tests, 44 server tests, both production builds, desktop/mobile
bubble comparisons, and 11 browser animation and scrolling checks.

server/README.md

@@ -106,3 +106,26 @@ When `chatId` is provided to completion endpoints, you can send full conversatio
 - User accounts + per-device API keys
 - Postgres support + migrations for prod
 - Attachments + embeddings + semantic search
+
+## Persistent Pi Agent
+
+Configure the backend with:
+
+```dotenv
+PI_AGENT_BASE_URL=http://pi-durable:8788
+PI_AGENT_API_KEY=<the Pi service's PI_API_KEY>
+```
+
+The base URL defaults to `http://pi-durable:8788` and has no `/v1` suffix. In Docker,
+attach Sybil's **server** container and Pi to the shared `agents` network so that
+`pi-durable` resolves privately. Supply the key through a private server environment
+file; it is never a `VITE_*` variable or browser setting. Keep the existing Sybil
+`ADMIN_TOKEN` authentication for clients.
+
+The Agent tab uses `/v1/agent`, `/v1/agent/messages`, and `/v1/agent/ws` to proxy the
+same persistent Pi root conversation across devices. Pi remains the source of
+truth for messages and background replies. Sybil stores only the shared,
+monotonically increasing read cursor in SQLite through `/v1/agent/read-state`;
+its migration is applied automatically at startup. The bundled nginx configuration
+forwards WebSocket upgrades. See `docs/api/rest.md` and
+`docs/api/streaming-chat.md` at the repository root for the client contracts.