fix(web): show settings on first load and hoist DemoProvider globally

Bug 1: On a fresh load with no saved config, RootLayout returned `null`
while a useEffect-driven `router.navigate()` fired, leaving a blank screen
until the user manually refreshed. Move the redirect into the root route's
`beforeLoad` so it happens synchronously during route resolution and the
settings form renders on first paint.

Bug 2: `DemoProvider` was mounted inside `RootLayout` only on the
non-settings branch, so any component reading `useDemo()` outside that
branch would throw "useDemoContext must be used within DemoProvider".
Hoist `<DemoProvider>` to `main.tsx` so the context is available app-wide.

Adds vitest + RTL setup with regression tests for both behaviours.

packages/web/vitest.config.ts

@@ -0,0 +1,24 @@
+import { defineConfig } from "vitest/config";
+import react from "@vitejs/plugin-react";
+import path from "node:path";
+import { fileURLToPath } from "node:url";
+
+const __dirname = path.dirname(fileURLToPath(import.meta.url));
+
+export default defineConfig({
+	plugins: [react()],
+	resolve: {
+		alias: {
+			"@": path.resolve(__dirname, "./src"),
+		},
+	},
+	define: {
+		__APP_VERSION__: JSON.stringify("0.0.0-test"),
+	},
+	test: {
+		environment: "jsdom",
+		globals: true,
+		setupFiles: ["./src/test/setup.ts"],
+		css: false,
+	},
+});