feat(web): Integrate M4-LLM error handling improvements

Port high-value features from work/m4-llm branch into develop's
security-hardened codebase:

- Separate LLM vs persistence error handling in useChat (shows
  assistant response even when save fails)
- Add structured error context logging with errorType, messagePreview,
  messageCount fields for debugging
- Enforce state invariant in useChatOverlay: cannot be minimized when
  closed
- Add onStorageError callback with user-friendly messages and
  per-error-type deduplication
- Add error logging to Chat imperative handle methods
- Create Chat.test.tsx with loadConversation failure mode tests

Skipped from work/m4-llm (superseded by develop):
- AbortSignal timeout (develop has centralized client timeout)
- Custom toast system (duplicates @mosaic/ui)
- ErrorBoundary (develop has its own)
- WebSocket typed events (develop's ref-based pattern is superior)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/web/src/components/chat/Chat.tsx

@@ -96,8 +96,13 @@ export const Chat = forwardRef<ChatRef, ChatProps>(function Chat(
 
   // Expose methods to parent via ref
   useImperativeHandle(ref, () => ({
-    loadConversation: async (conversationId: string): Promise<void> => {
-      await loadConversation(conversationId);
+    loadConversation: async (cId: string): Promise<void> => {
+      try {
+        await loadConversation(cId);
+      } catch (err) {
+        console.error("Failed to load conversation", { error: err, conversationId: cId });
+        throw err;
+      }
     },
     startNewConversation: (projectId?: string | null): void => {
       startNewConversation(projectId);
@@ -175,7 +180,11 @@ export const Chat = forwardRef<ChatRef, ChatProps>(function Chat(
 
   const handleSendMessage = useCallback(
     async (content: string) => {
-      await sendMessage(content);
+      try {
+        await sendMessage(content);
+      } catch (err) {
+        console.error("Error sending message:", err);
+      }
     },
     [sendMessage]
   );