Refactor screen names for consistency and rename component files to match updated naming conventions

app/Screens/JoinPrivateGamePage.js

@@ -0,0 +1,76 @@
+import React, { useState } from 'react';
+import { View, Text, TextInput, Pressable, StyleSheet } from 'react-native';
+import { useNavigation } from '@react-navigation/native';
+import usePrivateGameViewModel from '../ViewModel/usePrivateGameViewModel';
+import ScreenHeader from '../components/ScreenHeader';
+
+const JoinPrivateGamePage = () => {
+  const navigation = useNavigation();
+  const { joinCode, error, setJoinCode, joinWithCode } = usePrivateGameViewModel();
+  const [submitting, setSubmitting] = useState(false);
+
+  const handleJoinGame = async () => {
+    setSubmitting(true);
+    const group = await joinWithCode();
+    setSubmitting(false);
+    if (!group) {
+      return;
+    }
+    navigation.navigate('(routes)/game-lobby');
+  };
+
+  return (
+    <View style={styles.wrapper}>
+      <ScreenHeader title="Join Private Game" />
+      <View style={styles.container}>
+        <TextInput
+          style={styles.input}
+          placeholder="Enter Join Code"
+          autoCapitalize="characters"
+          maxLength={6}
+          value={joinCode}
+          onChangeText={setJoinCode}
+        />
+        <Pressable style={styles.button} onPress={handleJoinGame}>
+          <Text style={styles.buttonText}>{submitting ? 'Joining...' : 'Join Game'}</Text>
+        </Pressable>
+        {!!error && <Text style={styles.errorText}>{error}</Text>}
+      </View>
+    </View>
+  );
+};
+
+const styles = StyleSheet.create({
+  wrapper: {
+    flex: 1,
+    backgroundColor: '#ffffff',
+  },
+  container: {
+    flex: 1,
+    justifyContent: 'center',
+    padding: 20,
+    gap: 12,
+  },
+  input: {
+    borderWidth: 1,
+    borderColor: '#d1d5db',
+    borderRadius: 8,
+    paddingHorizontal: 12,
+    paddingVertical: 10,
+  },
+  button: {
+    backgroundColor: '#2563eb',
+    borderRadius: 8,
+    paddingVertical: 12,
+    alignItems: 'center',
+  },
+  buttonText: {
+    color: '#ffffff',
+    fontWeight: '600',
+  },
+  errorText: {
+    color: '#dc2626',
+  },
+});
+
+export default JoinPrivateGamePage;