fix(web): make streaming state per-session instead of global

Replace the global streaming ref with a streamingSessionId that
records which session is actively streaming. The streaming computed
now returns true only when the current session matches, so switching
sessions no longer leaks the generating indicator to unrelated sessions.

apps/web/src/store/chat-list.ts

@@ -97,7 +97,8 @@ export const useChatStore = defineStore('chat', () => {
   const { currentBotId, sessionId } = storeToRefs(selectionStore)
 
   const messages = reactive<ChatMessage[]>([])
-  const streaming = ref(false)
+  const streamingSessionId = ref<string | null>(null)
+  const streaming = computed(() => streamingSessionId.value !== null && streamingSessionId.value === sessionId.value)
   const sessions = ref<SessionSummary[]>([])
   const loading = ref(false)
   const loadingChats = ref(false)
@@ -334,7 +335,7 @@ export const useChatStore = defineStore('chat', () => {
     for (const msg of messages) {
       if (msg.streaming) msg.streaming = false
     }
-    streaming.value = false
+    streamingSessionId.value = null
   }
 
   // ---- Message list management ----
@@ -775,7 +776,6 @@ export const useChatStore = defineStore('chat', () => {
   async function createNewSession() {
     const bid = await ensureBot()
     if (!bid) return
-    // Enter draft state first. Session will be created lazily on first send.
     sessionId.value = null
     replaceMessages([])
   }
@@ -810,15 +810,14 @@ export const useChatStore = defineStore('chat', () => {
     if ((!trimmed && !attachments?.length) || streaming.value || !currentBotId.value) return
 
     loading.value = true
-    streaming.value = true
 
     try {
       await ensureActiveSession()
 
       const bid = currentBotId.value!
       const sid = sessionId.value!
+      streamingSessionId.value = sid
 
-      // Add user message
       const userBlocks: ContentBlock[] = []
       if (trimmed) userBlocks.push({ type: 'text', content: trimmed })
       if (attachments?.length) {
@@ -840,7 +839,6 @@ export const useChatStore = defineStore('chat', () => {
         streaming: false,
       })
 
-      // Add assistant placeholder
       messages.push({
         id: nextId(),
         role: 'assistant',
@@ -877,7 +875,7 @@ export const useChatStore = defineStore('chat', () => {
       await completion
 
       assistantMsg.streaming = false
-      streaming.value = false
+      streamingSessionId.value = null
       loading.value = false
       abortFn = null
       touchSession(sid)
@@ -898,7 +896,7 @@ export const useChatStore = defineStore('chat', () => {
         })
       }
       pendingAssistantStream = null
-      streaming.value = false
+      streamingSessionId.value = null
       loading.value = false
       abortFn = null
     }