Initial commit: Expo app with Better Auth integration

- Complete Expo React Native app setup with TypeScript
- Better Auth authentication system integration
- Secure storage implementation for session tokens
- Authentication flow with login/logout functionality
- API client configuration for backend communication
- Responsive UI components with themed styling
- Expo Router navigation setup
- Development configuration and scripts

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

components/auth/auth-button.tsx

@@ -0,0 +1,78 @@
+import { TouchableOpacity, StyleSheet, Alert, ActivityIndicator } from "react-native";
+import { router } from "expo-router";
+import { ThemedText } from "@/components/themed-text";
+import { useAuth } from "@/hooks/use-auth";
+import { authClient } from "@/lib/auth/client";
+import { useState } from "react";
+
+export function AuthButton() {
+  const { isAuthenticated, user, isLoading: sessionLoading } = useAuth();
+  const [isSigningOut, setIsSigningOut] = useState(false);
+
+  const handleSignOut = async () => {
+    setIsSigningOut(true);
+    try {
+      await authClient.signOut();
+      router.replace("/(auth)/login");
+    } catch (error: any) {
+      Alert.alert("登出失败", error?.message || "请稍后重试");
+    } finally {
+      setIsSigningOut(false);
+    }
+  };
+
+  const handleSignIn = () => {
+    router.push("/(auth)/login");
+  };
+
+  if (sessionLoading) {
+    return (
+      <TouchableOpacity style={styles.button} disabled>
+        <ActivityIndicator size="small" color="#007AFF" />
+      </TouchableOpacity>
+    );
+  }
+
+  if (isAuthenticated) {
+    return (
+      <TouchableOpacity
+        style={styles.button}
+        onPress={handleSignOut}
+        disabled={isSigningOut}
+      >
+        {isSigningOut ? (
+          <ActivityIndicator size="small" color="#FF3B30" />
+        ) : (
+          <ThemedText style={styles.signOutText}>
+            {user?.username ? `登出 (${user.username})` : "登出"}
+          </ThemedText>
+        )}
+      </TouchableOpacity>
+    );
+  }
+
+  return (
+    <TouchableOpacity style={styles.button} onPress={handleSignIn}>
+      <ThemedText style={styles.signInText}>登录</ThemedText>
+    </TouchableOpacity>
+  );
+}
+
+const styles = StyleSheet.create({
+  button: {
+    paddingHorizontal: 16,
+    paddingVertical: 8,
+    borderRadius: 8,
+    minWidth: 80,
+    alignItems: "center",
+    justifyContent: "center",
+  },
+  signInText: {
+    color: "#007AFF",
+    fontWeight: "600",
+  },
+  signOutText: {
+    color: "#FF3B30",
+    fontWeight: "600",
+  },
+});