fix: repair Mermaid diagram syntax errors and add PRD task plan

04 - Flows/Chat Flow.md

@@ -108,7 +108,7 @@ sequenceDiagram
 
     A->>FE_A: type & send
     FE_A->>BE: POST /api/chat/{id}/messages {content}
-    BE->>DB: chat.addMessage; metadata.lastActivity=now
+    BE->>DB: chat.addMessage and update metadata.lastActivity to now
     BE->>IO: emit chat-{id} 'new-message'
     IO-->>FE_A: 'new-message' (echo)
     IO-->>FE_B: 'new-message' (live)