fix(FN-2011): keep chat input responsive during streaming

- Make useChat and useQuickChat sendMessage synchronous and update consumers to call it without awaiting
- Allow ChatView and QuickChatFAB inputs to remain editable while responses stream
- Keep quick chat send disabled during active streaming to prevent concurrent sends
- Add hook and component tests for synchronous sendMessage and non-blocking input behavior

packages/dashboard/app/hooks/useChat.ts

@@ -58,7 +58,7 @@ export interface UseChatReturn {
   deleteSession: (id: string) => Promise<void>;
 
   // Message operations
-  sendMessage: (content: string) => Promise<void>;
+  sendMessage: (content: string) => void;
   loadMoreMessages: () => Promise<void>;
   hasMoreMessages: boolean;
 
@@ -291,7 +291,7 @@ export function useChat(projectId?: string): UseChatReturn {
 
   // Send a message
   const sendMessage = useCallback(
-    async (content: string) => {
+    (content: string) => {
       if (!activeSession) return;
 
       // Close any existing stream