[webview_flutter] Maybe fix flakiness of integration tests

[bparrishMines]

Fixes flutter/flutter#86757
Fixes flutter/flutter#90976
Fixes flutter/flutter#94750

From my understanding, the test failures were caused by one or more of the following:

1. The old implementation.
2. Ending a test with an expect using the completion matcher. I think it causes a race condition where the test will finish, but Native code would still be running. When running the test locally, one could see tests that have already been considered passing to still be logging.
3. Failed because reason 2 caused an error while another tests was running.
4. Not waiting for a url to finish loading before calling WebViewController.currentUrl.

The code below was used in packages/webview_flutter/webview_flutter/example and packages/webview_flutter/webview_flutter_android/example to test flakiness. It runs the integration tests 10 times and records the number of failures of each test.

import 'dart:io';

final Map<String, int> failedTests = <String, int>{};
int allTestsPassCount = 0;

const int runCount = 10;

void main() async {
  for (int i = 0; i < runCount; i++) {
    final Process process = await Process.start(
      'flutter',
      '--no-color test -d emulator-5554 --timeout 240s integration_test/webview_flutter_test.dart'
          .split(' '),
    );

    process.stdout.forEach((List<int> data) {
      stdout.add(data);
      final String output = String.fromCharCodes(data);

      //00:43 +1 -2: test 3 [E]
      if (output.contains('[E]')) {
        final String? testName = RegExp(
          r'(?<=\d+:\d+ [0-9\+\-\s]+: ).+(?= \[E\])',
        ).stringMatch(output);

        if (testName == null) {
          print('FAILED TO PARSE TEST NAME: $output');
        } else {
          failedTests.putIfAbsent(testName, () => 0);
          failedTests[testName] = failedTests[testName]! + 1;
        }
      }

      if (output.contains('All tests passed!')) {
        allTestsPassCount++;
      }
    });
    process.stderr.forEach((List<int> data) {
      stderr.add(data);
    });
    await process.exitCode;

    print('CURRENT TEST FAILURE COUNTS:');
    print(failedTests);
  }

  print('ALL TESTS PASS COUNT: $allTestsPassCount');
  print('Desired count: $runCount');
}

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read and followed the relevant style guides and ran the auto-formatter. (Unlike the flutter/flutter repo, the flutter/plugins repo does use dart format.)
• I signed the CLA.
• The title of the PR starts with the name of the plugin surrounded by square brackets, e.g. [shared_preferences]
• I listed at least one issue that this PR fixes in the description above.
• I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy, or this PR is exempt from version changes.
• I updated CHANGELOG.md to add a description of the change, following repository CHANGELOG style.
• I updated/added relevant documentation (doc comments with ///).
• I added new tests to check the change I am making, or this PR is test-exempt.
• All existing and new tests are passing.

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[stuartmorgan-g]

Nice! LGTM