feat(#42): Implement persistent Jarvis chat overlay

Add a persistent chat overlay accessible from any authenticated view.
The overlay wraps the existing Chat component and adds state management,
keyboard shortcuts, and responsive design.

Features:
- Three states: Closed (floating button), Open (full panel), Minimized (header)
- Keyboard shortcuts:
  - Cmd/Ctrl + K: Open chat (when closed)
  - Escape: Minimize chat (when open)
  - Cmd/Ctrl + Shift + J: Toggle chat panel
- State persistence via localStorage
- Responsive design (full-width mobile, sidebar desktop)
- PDA-friendly design with calm colors
- 32 comprehensive tests (14 hook tests + 18 component tests)

Files added:
- apps/web/src/hooks/useChatOverlay.ts
- apps/web/src/hooks/useChatOverlay.test.ts
- apps/web/src/components/chat/ChatOverlay.tsx
- apps/web/src/components/chat/ChatOverlay.test.tsx

Files modified:
- apps/web/src/components/chat/index.ts (added export)
- apps/web/src/app/(authenticated)/layout.tsx (integrated overlay)

All tests passing (490 tests, 50 test files)
All lint checks passing
Build succeeds

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

apps/web/src/hooks/useChatOverlay.ts

@@ -0,0 +1,109 @@
+/**
+ * @file useChatOverlay.ts
+ * @description Hook for managing the global chat overlay state
+ */
+
+import { useState, useEffect, useCallback } from "react";
+
+interface ChatOverlayState {
+  isOpen: boolean;
+  isMinimized: boolean;
+}
+
+interface UseChatOverlayResult extends ChatOverlayState {
+  open: () => void;
+  close: () => void;
+  minimize: () => void;
+  expand: () => void;
+  toggle: () => void;
+  toggleMinimize: () => void;
+}
+
+const STORAGE_KEY = "chatOverlayState";
+
+const DEFAULT_STATE: ChatOverlayState = {
+  isOpen: false,
+  isMinimized: false,
+};
+
+/**
+ * Load state from localStorage
+ */
+function loadState(): ChatOverlayState {
+  if (typeof window === "undefined") {
+    return DEFAULT_STATE;
+  }
+
+  try {
+    const stored = window.localStorage.getItem(STORAGE_KEY);
+    if (stored) {
+      return JSON.parse(stored) as ChatOverlayState;
+    }
+  } catch (error) {
+    console.warn("Failed to load chat overlay state from localStorage:", error);
+  }
+
+  return DEFAULT_STATE;
+}
+
+/**
+ * Save state to localStorage
+ */
+function saveState(state: ChatOverlayState): void {
+  if (typeof window === "undefined") {
+    return;
+  }
+
+  try {
+    window.localStorage.setItem(STORAGE_KEY, JSON.stringify(state));
+  } catch (error) {
+    console.warn("Failed to save chat overlay state to localStorage:", error);
+  }
+}
+
+/**
+ * Custom hook for managing chat overlay state
+ * Persists state to localStorage for consistency across page refreshes
+ */
+export function useChatOverlay(): UseChatOverlayResult {
+  const [state, setState] = useState<ChatOverlayState>(loadState);
+
+  // Persist state changes to localStorage
+  useEffect(() => {
+    saveState(state);
+  }, [state]);
+
+  const open = useCallback(() => {
+    setState({ isOpen: true, isMinimized: false });
+  }, []);
+
+  const close = useCallback(() => {
+    setState((prev) => ({ ...prev, isOpen: false }));
+  }, []);
+
+  const minimize = useCallback(() => {
+    setState((prev) => ({ ...prev, isMinimized: true }));
+  }, []);
+
+  const expand = useCallback(() => {
+    setState((prev) => ({ ...prev, isMinimized: false }));
+  }, []);
+
+  const toggle = useCallback(() => {
+    setState((prev) => ({ ...prev, isOpen: !prev.isOpen }));
+  }, []);
+
+  const toggleMinimize = useCallback(() => {
+    setState((prev) => ({ ...prev, isMinimized: !prev.isMinimized }));
+  }, []);
+
+  return {
+    ...state,
+    open,
+    close,
+    minimize,
+    expand,
+    toggle,
+    toggleMinimize,
+  };
+}