Unexpected "uncaught" exception passed to `onError` of `runZonedGuarded()` despite `try`/`catch` - flutter

Question

Given the following complete minimal example run on Flutter 3.7.3 and Dart 2.19.2:
import 'dart:async';
import 'package:flutter/material.dart';
import 'package:http/http.dart' as http;
void main() {
WidgetsFlutterBinding.ensureInitialized();
runZonedGuarded(() {
runApp(const MyApp());
}, (error, stack) {
print('onError: $error\n$stack');
});
}
class MyApp extends StatelessWidget {
const MyApp({super.key});
#override Widget build(BuildContext context) => const MaterialApp(home: MyHomePage());
}
class MyHomePage extends StatefulWidget {
const MyHomePage({super.key});
#override State<MyHomePage> createState() => _MyHomePageState();
}
class _MyHomePageState extends State<MyHomePage> {
final http.Client _httpClient = http.Client();
#override
void initState() {
super.initState();
request().then((value) => print('then')).catchError((error) => print('catchError'));
}
Future<void> request() async {
try {
var request = http.Request('POST', Uri.parse('http://192.168.0.1'));
await _httpClient.send(request);
}
catch (error) {
print('catch: $error');
}
}
#override
Widget build(BuildContext context) {
return Scaffold(
body: const Center(
child: Text('Push the button'),
),
floatingActionButton: FloatingActionButton(
onPressed: () => _httpClient.close(), // this leads to the exceptions
child: const Icon(Icons.add),
),
);
}
}
When the "+" button on the UI is pressed, a SocketException is both passed to the onError callback of the runZonedGuarded() and also the catch block of the HTTP request.
The console output is:
Restarted application in 720ms.
flutter: onError: SocketException: Connection attempt cancelled, host: 192.168.0.1, port: 80
#0 _NativeSocket.startConnect (dart:io-patch/socket_patch.dart:694:35)
#1 _RawSocket.startConnect (dart:io-patch/socket_patch.dart:1855:26)
#2 RawSocket.startConnect (dart:io-patch/socket_patch.dart:27:23)
#3 Socket._startConnect (dart:io-patch/socket_patch.dart:2078:22)
#4 Socket.startConnect (dart:io/socket.dart:763:21)
#5 _ConnectionTarget.connect (dart:_http/http_impl.dart:2466:20)
#6 _HttpClient._getConnection.connect (dart:_http/http_impl.dart:2906:12)
#7 _HttpClient._getConnection (dart:_http/http_impl.dart:2911:12)
#8 _HttpClient._openUrl (dart:_http/http_impl.dart:2766:12)
#9 _HttpClient.openUrl (dart:_http/http_impl.dart:2604:7)
#10 IOClient.send
#11 _MyHomePageState.request
#12 _MyHomePageState.initState
#13 StatefulElement._firstBuild
#14 ComponentElement.mount
--- 8< ---
#384 Element.inflateWidget (package:flutter/src/widgets/framework.dart:3953:16)<…>
flutter: catch: Connection attempt cancelled, host: 192.168.0.1, port: 80
flutter: then
What I would like to know is...
Why are two apparently identical exceptions raised rather than one? (The two exception objects have different identity hash codes, but otherwise appear equivalent.)
Why, if the exception passed to onError is considered uncaught, does the stack trace for that very exception clearly show the try/catch block as an ancestor?
How can I catch the uncaught exception? So that it can be dealt with and not be uncaught?
Note: It's intentional for this demonstration that the HTTP request and subsequent client closure results in a SocketException. I'm not asking why this results in a SocketException. I'm asking why there are two exceptions, one of which is considered uncaught, despite the use of try/catch.
Note 2: Run on iOS device.