DevTools integration test flakes

The DevTools integration tests have been getting flaky.

devtools_extensions_test.dart

https://github.com/flutter/devtools/actions/runs/18566177330/job/52927948189

```
FlutterDriveProcess - Launching integration_test/test/live_connection/devtools_extensions_test.dart on Web Server in debug mode...
FlutterDriveProcess - Waiting for connection from debug service on Web Server... 67.1s
FlutterDriveProcess - integration_test/test/live_connection/devtools_extensions_test.dart is being served at http://localhost:49514
FlutterDriveProcess - The web-server device requires the Dart Debug Chrome extension for debugging. Consider using the Chrome or Edge devices for an improved development workflow.
ChromeDriver - [1760628606.940][SEVERE]: Timed out receiving message from renderer: 298.218
ChromeDriver - [1760628606.968][SEVERE]: Timed out receiving message from renderer: 298.218
FlutterDriveProcess - Unhandled exception:
FlutterDriveProcess - TimeoutException (500): timeout: Timed out receiving message from renderer: 298.218
FlutterDriveProcess - (Session info: chrome=140.0.7339.207)
FlutterDriveProcess - #0 parseW3cResponse (package:webdriver/src/handler/w3c/utils.dart:87:9)
FlutterDriveProcess - #1 W3cNavigationHandler.parseNavigateToResponse (package:webdriver/src/handler/w3c/navigation.dart:26:5)
FlutterDriveProcess - #2 AsyncRequestClient.send (package:webdriver/src/common/request_client.dart:96:32)
FlutterDriveProcess -
FlutterDriveProcess - #3 FlutterWebConnection.connect (package:flutter_driver/src/driver/web_driver.dart:301:5)
FlutterDriveProcess -
FlutterDriveProcess - #4 WebFlutterDriver.connectWeb (package:flutter_driver/src/driver/web_driver.dart:99:45)
FlutterDriveProcess -
FlutterDriveProcess - #5 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/test_driver/integration_test.dart:21:18)
FlutterDriveProcess -
FlutterDriveProcess - Application finished.
Unhandled exception:
Exception: Unhandled exception:
TimeoutException (500): timeout: Timed out receiving message from renderer: 298.218
(Session info: chrome=140.0.7339.207)
#0 parseW3cResponse (package:webdriver/src/handler/w3c/utils.dart:87:9)
#1 W3cNavigationHandler.parseNavigateToResponse (package:webdriver/src/handler/w3c/navigation.dart:26:5)
#2 AsyncRequestClient.send (package:webdriver/src/common/request_client.dart:96:32)

#3 FlutterWebConnection.connect (package:flutter_driver/src/driver/web_driver.dart:301:5)

#4 WebFlutterDriver.connectWeb (package:flutter_driver/src/driver/web_driver.dart:99:45)

#5 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/test_driver/integration_test.dart:21:18)

#0 IntegrationTestRunner.run.runTest (package:devtools_shared/src/test/integration_test_runner.dart:154:11)

#1 IntegrationTestRunner.run (package:devtools_shared/src/test/integration_test_runner.dart:160:5)

#2 runFlutterIntegrationTest (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/test_infra/run/run_test.dart:121:5)

#3 _runTest (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/run_tests.dart:84:3)

#4 runOneOrManyTests (package:devtools_shared/src/test/integration_test_runner.dart:354:9)

#5 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/run_tests.dart:53:3)

Error: Process completed with exit code 255.
```

network_screen_test.dart

https://github.com/flutter/devtools/actions/runs/18568989429/job/52937864918

```
FlutterDriveProcess - Launching integration_test/test/live_connection/network_screen_test.dart on Web Server in debug mode...
FlutterDriveProcess - Waiting for connection from debug service on Web Server... 50.8s
FlutterDriveProcess - integration_test/test/live_connection/network_screen_test.dart is being served at http://localhost:49478
FlutterDriveProcess - The web-server device requires the Dart Debug Chrome extension for debugging. Consider using the Chrome or Edge devices for an improved development workflow.
FlutterDriveProcess - Debug service listening on ws://127.0.0.1:44456/vNmLRKxvmGU=
FlutterDriveProcess - A Dart VM Service on Web Server is available at: http://127.0.0.1:44456/vNmLRKxvmGU=
ChromeDriver - [1760634965.294][SEVERE]: Timed out receiving message from renderer: 30.000
FlutterDriveProcess - Unhandled exception:
FlutterDriveProcess - DriverError: Driver extension has not been initialized correctly.
FlutterDriveProcess - If the test uses a custom VM service extension, make sure it conforms to the protocol used by package:integration_test and package:flutter_driver.
FlutterDriveProcess - If the test uses VM service extensions provided by the Flutter SDK, then this error is likely caused by a bug in Flutter. Please report it by filing a bug on GitHub:
FlutterDriveProcess - https://github.com/flutter/flutter/issues/new?template=02_bug.yml
FlutterDriveProcess - Original error: ScriptTimeoutException (500): script timeout
FlutterDriveProcess - (Session info: chrome=140.0.7339.207)
FlutterDriveProcess - Original stack trace:
FlutterDriveProcess - #0 parseW3cResponse (package:webdriver/src/handler/w3c/utils.dart:78:9)
FlutterDriveProcess - #1 W3cCoreHandler.parseExecuteResponse (package:webdriver/src/handler/w3c/core.dart:59:19)
FlutterDriveProcess - #2 WebDriver.execute. (package:webdriver/src/async/web_driver.dart:264:37)
FlutterDriveProcess - #3 AsyncRequestClient.send (package:webdriver/src/common/request_client.dart:96:32)
FlutterDriveProcess -
FlutterDriveProcess - #4 FlutterWebConnection.sendCommand (package:flutter_driver/src/driver/web_driver.dart:316:7)
FlutterDriveProcess -
FlutterDriveProcess - #5 WebFlutterDriver.sendCommand (package:flutter_driver/src/driver/web_driver.dart:126:14)
FlutterDriveProcess -
FlutterDriveProcess - #6 FlutterDriver.requestData (package:flutter_driver/src/driver/driver.dart:573:7)
FlutterDriveProcess -
FlutterDriveProcess - #7 integrationDriver (package:integration_test/integration_test_driver_extended.dart:87:25)
FlutterDriveProcess -
FlutterDriveProcess - #8 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/test_driver/integration_test.dart:22:3)
FlutterDriveProcess -
FlutterDriveProcess -
FlutterDriveProcess -
FlutterDriveProcess - #0 FlutterWebConnection.sendCommand (package:flutter_driver/src/driver/web_driver.dart:318:7)
FlutterDriveProcess -
FlutterDriveProcess - #1 WebFlutterDriver.sendCommand (package:flutter_driver/src/driver/web_driver.dart:126:14)
FlutterDriveProcess -
FlutterDriveProcess - #2 FlutterDriver.requestData (package:flutter_driver/src/driver/driver.dart:573:7)
FlutterDriveProcess -
FlutterDriveProcess - #3 integrationDriver (package:integration_test/integration_test_driver_extended.dart:87:25)
FlutterDriveProcess -
FlutterDriveProcess - #4 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/test_driver/integration_test.dart:22:3)
FlutterDriveProcess -
FlutterDriveProcess - Application finished.
Unhandled exception:
Exception: Unhandled exception:
DriverError: Driver extension has not been initialized correctly.
If the test uses a custom VM service extension, make sure it conforms to the protocol used by package:integration_test and package:flutter_driver.
If the test uses VM service extensions provided by the Flutter SDK, then this error is likely caused by a bug in Flutter. Please report it by filing a bug on GitHub:
https://github.com/flutter/flutter/issues/new?template=02_bug.yml
Original error: ScriptTimeoutException (500): script timeout
(Session info: chrome=140.0.7339.207)
Original stack trace:
#0 parseW3cResponse (package:webdriver/src/handler/w3c/utils.dart:78:9)
#1 W3cCoreHandler.parseExecuteResponse (package:webdriver/src/handler/w3c/core.dart:59:19)
#2 WebDriver.execute. (package:webdriver/src/async/web_driver.dart:264:37)
#3 AsyncRequestClient.send (package:webdriver/src/common/request_client.dart:96:32)

#4 FlutterWebConnection.sendCommand (package:flutter_driver/src/driver/web_driver.dart:316:7)

#5 WebFlutterDriver.sendCommand (package:flutter_driver/src/driver/web_driver.dart:126:14)

#6 FlutterDriver.requestData (package:flutter_driver/src/driver/driver.dart:573:7)

#7 integrationDriver (package:integration_test/integration_test_driver_extended.dart:87:25)

#8 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/test_driver/integration_test.dart:22:3)

#0 FlutterWebConnection.sendCommand (package:flutter_driver/src/driver/web_driver.dart:318:7)

#1 WebFlutterDriver.sendCommand (package:flutter_driver/src/driver/web_driver.dart:126:14)

#2 FlutterDriver.requestData (package:flutter_driver/src/driver/driver.dart:573:7)

#3 integrationDriver (package:integration_test/integration_test_driver_extended.dart:87:25)

#4 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/test_driver/integration_test.dart:22:3)

#0 IntegrationTestRunner.run.runTest (package:devtools_shared/src/test/integration_test_runner.dart:154:11)

#1 IntegrationTestRunner.run (package:devtools_shared/src/test/integration_test_runner.dart:160:5)

#2 runFlutterIntegrationTest (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/test_infra/run/run_test.dart:121:5)

#3 _runTest (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/run_tests.dart:84:3)

#4 runOneOrManyTests (package:devtools_shared/src/test/integration_test_runner.dart:354:9)

#5 main (file:///Users/runner/work/devtools/devtools/packages/devtools_app/integration_test/run_tests.dart:53:3)

Error: Process completed with exit code 255.
```