Add E2E testing infrastructure with WebdriverIO + Appium

Set up E2E test framework for Android using WebdriverIO, Appium, and
UiAutomator2. Add testID props to key components (AuthButton, BaseButton,
ChatBubble, CustomTextInput, ProposedEventCard) and apply testIDs to
login screen, chat screen, tab bar, and settings. Include initial tests
for app launch detection and login flow validation. Update CLAUDE.md
with E2E docs.

apps/client/src/app/(tabs)/settings.tsx

@@ -20,6 +20,7 @@ const handleLogout = async () => {
 const SettingsButton = (props: BaseButtonProps) => {
   return (
     <BaseButton
+      testID={props.testID}
       onPress={props.onPress}
       solid={props.solid}
       className={"w-11/12"}
@@ -214,7 +215,7 @@ const Settings = () => {
     <BaseBackground>
       <SimpleHeader text="Settings" />
       <View className="flex items-center mt-4">
-        <SettingsButton onPress={handleLogout} solid={true}>
+        <SettingsButton testID="settings-logout-button" onPress={handleLogout} solid={true}>
           <Ionicons name="log-out-outline" size={24} color={theme.primeFg} />{" "}
           Logout
         </SettingsButton>