[CP-stable][web] Don't close image source too early

[flutteractionsbot]

This pull request is created by automatic cherry pick workflow
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Issue Links:

flutter/flutter#160199
flutter/flutter#158093

Changelog Description:

Fix a regression that causes some images on the web to render blank.

Impact Description:

Some images are showing as a blank rectangle in the Stable release of Flutter Web.

Workaround:

No workaround as far as I know.

Risk:

What is the risk level of this cherry-pick?

• Low
• Medium
• High

Test Coverage:

Are you confident that your fix is well-tested by automated tests?

• Yes
• No

Validation Steps:

Make sure there's an image rendered in the following app:

import 'package:flutter/material.dart';

void main() => runApp(const MyApp());

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    var title = 'Web Images';

    return MaterialApp(
      title: title,
      home: Scaffold(
        appBar: AppBar(
          title: Text(title),
        ),
        body: Image.network(
          'https://picsum.photos/250?image=9',
          cacheHeight: 100,
        ),
      ),
    );
  }
}

[flutteractionsbot]

@mdebbar please fill out the PR description above, afterwards the release team will review this request.