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.

docs/api/rest.md

@@ -562,3 +562,73 @@ Behavior notes:
 ```
 
 For streaming contracts, see `docs/api/streaming-chat.md`.
+
+## Persistent Agent Room
+
+The Agent tab connects to one persistent Pi root conversation. Pi owns its messages,
+background work, and history; these endpoints do not create ordinary Sybil chats or
+copy the transcript into the Sybil message database. All endpoints use normal Sybil
+REST authentication. The server connects privately to `PI_AGENT_BASE_URL` (default
+`http://pi-durable:8788`) using `PI_AGENT_API_KEY`. The Pi key never reaches browsers.
+
+### `GET /v1/agent`
+
+Returns the Pi room descriptor: `id`, `title`, `type: "persistent-agent"`, `model`,
+`protocol: "pi-room.v1"`, `activity`, and `websocket: "/v1/agent/ws"`. The socket path
+is relative to the API base, so web deployments use `/api/v1/agent/ws`. Missing Pi
+configuration returns 503; an unreachable Pi server or malformed upstream JSON
+returns 502.
+
+### `GET /v1/agent/messages`
+
+Query parameters: optional `after` or `before` (mutually exclusive nonnegative
+numeric cursor strings), and `limit` (1–200). Without a cursor, returns recent
+history. `after` catches up forward; `before` loads earlier history.
+
+```json
+{
+  "conversationId": "1",
+  "messages": [{ "id": "outbound:43", "createdAt": "2026-10-14T18:00:00.000Z", "role": "assistant", "content": "The task finished.", "name": "Pi", "metadata": { "kind": "message", "entryId": 43, "status": "complete" } }],
+  "cursor": "43",
+  "beforeCursor": "43",
+  "hasMore": false
+}
+```
+
+Messages use `user`, `assistant`, and `tool` roles. Tools use
+`metadata.kind: "tool_call"` and stable IDs; merge by message `id`, since later
+pages can update initiated tools to completed or failed. Internal worker reports,
+event prompts, and model reasoning are excluded. Cursors refer to underlying
+durable entries and can advance without visible messages. Use returned cursors;
+do not derive them from message IDs. `limit` bounds source entries, not displayed
+messages.
+
+### `POST /v1/agent/messages`
+
+Body: `{ "content": "Check the oven", "requestId": "client-generated-uuid" }`.
+Content must contain non-whitespace text and is limited to 40,000 characters;
+`requestId` is required (1–256 characters). Preserve the ID when retrying uncertain
+network results. The proxy fixes `channel: "sybil"`, `whenBusy: "followUp"`, and
+`wait: false`.
+
+Returns Pi's `202 Accepted` receipt, including `id` (submission ID), `status`, and
+`messageId` such as `inbound:sybil:client-generated-uuid`. This is admission, not
+completion: watch the room for answers, including unsolicited later replies.
+Multiple requests can be accepted while Pi works. Attachments are not yet supported.
+The proxy verifies successful receipts contain a positive submission ID, a known
+status (`queued`, `placed`, `done`, or `unanswered`), and the expected `messageId`.
+Invalid receipts return 502; delivery remains uncertain, so retry using the original
+`requestId` to avoid creating a duplicate message.
+
+### `GET /v1/agent/read-state`
+### `PUT /v1/agent/read-state`
+
+GET returns `{ "cursor": "43", "updatedAt": "2026-10-14T18:00:00.000Z" }`.
+Initially: `{ "cursor": "0", "updatedAt": null }`. PUT takes
+`{ "cursor": "43" }` and returns the same shape. The cursor is shared across this
+personal installation and persisted in SQLite. Atomic, monotonic updates prevent
+a stale browser from lowering a cursor saved by another browser. Advance it only
+after showing the corresponding history; poll it to reconcile unread indicators
+across clients. Agent REST responses use `Cache-Control: no-store`.
+
+See the persistent Agent WebSocket section in `streaming-chat.md` for live updates.