fix(expo-router): pickDefaultScreen prefers a group with an index leaf

When the user-driven redirect after sign-in landed on the root with
href '/', our Stack matched the empty segment, fell back to
\`screens[0]\` — which is the FIRST <Stack.Screen> declared in
akari's root layout: '(auth)'. Effect: every successful login
bounced the user right back to the auth choice screen.

Real expo-router treats group segments \`(name)\` as URL-transparent:
'/' resolves through whatever group has an 'index' leaf. For akari
that's '(tabs)' (\`app/(tabs)/index/index.tsx\`), not '(auth)'
(which only has signin/oauth/password siblings, no index).

Add pickDefaultScreen(screens, base): walks the screens, picks the
first group whose corresponding file-system route table entry has
an index child (\`<group>/index\`, \`<group>/index/_layout\`, or
\`<group>/index/index\`). Falls back to \`screens[0]\` when no group
match — keeps existing apps (smoke-demo, expo-router-tabs.tsx, etc.)
unchanged, since they have no route table registered.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: ImLunaHey

packages/@lucid-softworks/react-native-linux-expo/expo-router.js

@@ -209,6 +209,33 @@ function effectiveSegment(pathname, base) {
   return p.split('/')[0] || '';
 }
 
+// When the pathname doesn't pick a screen by name (typically because
+// the user just navigated to `/` and the layout has only group screens
+// like `(auth)` / `(tabs)`), pick the one whose group has an `index`
+// route in our file-system table. Real expo-router treats group
+// segments as URL-transparent — `/` resolves through the group that
+// has an index leaf. For akari that's `(tabs)` (it has
+// `app/(tabs)/index/index.tsx`), NOT `(auth)`. Without this lookup we
+// always fall back to `screens[0]`, which kept routing post-login
+// back to the auth choice screen.
+function pickDefaultScreen(screens, base) {
+  const routes = typeof globalThis !== 'undefined' ? globalThis.__expoRouterRoutes : null;
+  if (routes) {
+    for (const s of screens) {
+      if (!s.name || s.name[0] !== '(' || s.name[s.name.length - 1] !== ')') continue;
+      const groupPath = (base ? base : '') + '/' + s.name;
+      if (
+        routes[groupPath + '/index'] ||
+        routes[groupPath + '/index/_layout'] ||
+        routes[groupPath + '/index/index']
+      ) {
+        return s;
+      }
+    }
+  }
+  return screens[0];
+}
+
 // ────────────────────────────────────────────────────────────────
 // Stack — renders the screen whose `name` matches the current
 // pathname segment. Stack.Screen is config-only (no own render).
@@ -222,7 +249,7 @@ function Stack({children, screenOptions}) {
   const base = React.useContext(RouteBaseContext);
   const screens = collectScreens(children, Stack.Screen, base);
   const seg = effectiveSegment(ctx.pathname, base) || 'index';
-  const match = screens.find(s => s.name === seg) ?? screens[0];
+  const match = screens.find(s => s.name === seg) ?? pickDefaultScreen(screens, base);
   const headerShown = match?.options?.headerShown ?? screenOptions?.headerShown ?? true;
   const tree = React.createElement(
     View,
@@ -264,7 +291,7 @@ function Tabs({children, screenOptions}) {
   const base = React.useContext(RouteBaseContext);
   const screens = collectScreens(children, Tabs.Screen, base);
   const seg = effectiveSegment(ctx.pathname, base) || screens[0]?.name;
-  const active = screens.find(s => s.name === seg) ?? screens[0];
+  const active = screens.find(s => s.name === seg) ?? pickDefaultScreen(screens, base);
   const activeColor =
     active?.options?.tabBarActiveTintColor ?? screenOptions?.tabBarActiveTintColor ?? '#2563eb';
   const inactiveColor =