Add splash screen handling and logo to HomeScreen, update dependencies

src/screens/HomeScreen.js

@@ -1,5 +1,5 @@
 import React from 'react';
-import { ScrollView, Text, TouchableOpacity, View } from 'react-native';
+import { ScrollView, Text, TouchableOpacity, View, Image } from 'react-native';
 import TopControls from '../components/TopControls';
 
 export default function HomeScreen({
@@ -18,6 +18,10 @@ export default function HomeScreen({
   return (
     <View style={[styles.root, { backgroundColor: theme.bg }]}>
       <ScrollView contentContainerStyle={styles.scroll} keyboardShouldPersistTaps="handled">
+        <Image
+          source={require('../../assets/icon.png')}
+          style={[styles.logo, pinkMode && { borderColor: theme.accent, borderWidth: 2 }]}
+        />
         <Text
           style={[
             styles.title,