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Skipped from work/m4-llm (superseded by develop):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/hooks/useChat.ts

@@ -208,12 +208,33 @@ export function useChat(options: UseChatOptions = {}): UseChatReturn {
           ? generateTitle(content)
           : (conversationTitle ?? "Chat Conversation");
 
-        // Save conversation
-        await saveConversation(finalMessages, title);
+        // Save conversation (separate error handling from LLM errors)
+        try {
+          await saveConversation(finalMessages, title);
+        } catch (saveErr) {
+          const saveErrorMsg =
+            saveErr instanceof Error ? saveErr.message : "Unknown persistence error";
+          setError(`Message sent but failed to save: ${saveErrorMsg}`);
+          console.error("Failed to save conversation", {
+            error: saveErr,
+            errorType: "PERSISTENCE_ERROR",
+            conversationId,
+          });
+        }
       } catch (err) {
         const errorMsg = err instanceof Error ? err.message : "Failed to send message";
         setError(errorMsg);
         onError?.(err instanceof Error ? err : new Error(errorMsg));
+        console.error("Failed to send chat message", {
+          error: err,
+          errorType: "LLM_ERROR",
+          conversationId,
+          messageLength: content.length,
+          messagePreview: content.substring(0, 50),
+          model,
+          messageCount: messagesRef.current.length,
+          timestamp: new Date().toISOString(),
+        });
 
         // Add error message to chat
         const errorMessage: Message = {