Refactor App.tsx from god component to context-based architecture

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/web/src/contexts/side-panel-context.tsx

@@ -0,0 +1,21 @@
+import { createContext, type ReactNode, useContext } from "react";
+import { useSidePanelState } from "../hooks/use-side-panel-state.js";
+
+type SidePanelContextValue = ReturnType<typeof useSidePanelState>;
+
+const SidePanelContext = createContext<SidePanelContextValue | null>(null);
+
+export function SidePanelProvider({ children }: { children: ReactNode }) {
+	const value = useSidePanelState();
+	return (
+		<SidePanelContext.Provider value={value}>
+			{children}
+		</SidePanelContext.Provider>
+	);
+}
+
+export function useSidePanelContext(): SidePanelContextValue {
+	const ctx = useContext(SidePanelContext);
+	if (!ctx) throw new Error("useSidePanelContext requires SidePanelProvider");
+	return ctx;
+}