feat(web): use a global WebSocket for Pico chat sessions (#1507)

- centralize Pico chat connection and session state in a shared store
- move chat lifecycle control out of usePicoChat
- hydrate and restore the active session across the app

web/frontend/src/store/chat.ts

@@ -0,0 +1,62 @@
+import { atom, getDefaultStore } from "jotai"
+
+import {
+  getInitialActiveSessionId,
+  writeStoredSessionId,
+} from "@/lib/pico-chat-state"
+
+export interface ChatMessage {
+  id: string
+  role: "user" | "assistant"
+  content: string
+  timestamp: number | string
+}
+
+export type ConnectionState =
+  | "disconnected"
+  | "connecting"
+  | "connected"
+  | "error"
+
+export interface ChatStoreState {
+  messages: ChatMessage[]
+  connectionState: ConnectionState
+  isTyping: boolean
+  activeSessionId: string
+  hasHydratedActiveSession: boolean
+}
+
+type ChatStorePatch = Partial<ChatStoreState>
+
+const DEFAULT_CHAT_STATE: ChatStoreState = {
+  messages: [],
+  connectionState: "disconnected",
+  isTyping: false,
+  activeSessionId: getInitialActiveSessionId(),
+  hasHydratedActiveSession: false,
+}
+
+export const chatAtom = atom<ChatStoreState>(DEFAULT_CHAT_STATE)
+
+const store = getDefaultStore()
+
+export function getChatState() {
+  return store.get(chatAtom)
+}
+
+export function updateChatStore(
+  patch:
+    | ChatStorePatch
+    | ((prev: ChatStoreState) => ChatStorePatch | ChatStoreState),
+) {
+  store.set(chatAtom, (prev) => {
+    const nextPatch = typeof patch === "function" ? patch(prev) : patch
+    const next = { ...prev, ...nextPatch }
+
+    if (next.activeSessionId !== prev.activeSessionId) {
+      writeStoredSessionId(next.activeSessionId)
+    }
+
+    return next
+  })
+}

web/frontend/src/store/index.ts

@@ -1 +1,2 @@
 export * from "./gateway"
+export * from "./chat"