DWDS error when running DevTools integration tests

DWDS error when running DevTools integration tests.

One of our integration tests recently failed in CI ([run link](https://github.com/flutter/devtools/actions/runs/12798927680/job/35683997493)) with the following error:

```
result {"result":"false","failureDetails":["{\"methodName\":\"end to end extensions flow\",\"details\":\"══╡ EXCEPTION CAUGHT BY FLUTTER TEST FRAMEWORK ╞═════════════════\\nThe following RPCError was thrown running a test:\\next.flutter.inspector.structuredErrors: (-32603) Unexpected DWDS\\nerror for callServiceExtension: WipError -32000 Promise was\\ncollected\\n\\nWhen the exception was thrown, this was the stack:\\ndart-sdk/lib/_internal/js_dev_runtime/patch/core_patch.dart 748:28 get current\\npackages/vm_service/src/snapshot_graph.dart.js 1870:41 new\\npackages/vm_service/src/snapshot_graph.dart.js 2530:23 \\npackages/vm_service/src/snapshot_graph.dart.js 2538:76 [_call]\\npackages/vm_service/src/snapshot_graph.dart.js 2476:27 callServiceExtension\\npackages/devtools_app_shared/src/service/service_extension_manager.dart.js 1042:91 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 622:19 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 647:23 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 541:3 _asyncStartSync\\npackages/devtools_app_shared/src/service/service_extension_manager.dart.js 1049:40 call\\npackages/devtools_app_shared/src/service/service_extension_manager.dart.js 1084:62 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 622:19 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 647:23 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 541:3 _asyncStartSync\\npackages/devtools_app_shared/src/service/service_extension_manager.dart.js 1157:30 callExtension\\npackages/devtools_app_shared/src/service/service_extension_manager.dart.js 1186:51 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 622:19 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 647:23 \\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 593:31 \\ndart-sdk/lib/async/zone.dart 1538:47 _rootRunUnary\\ndart-sdk/lib/async/zone.dart 1429:19 runUnary\\ndart-sdk/lib/async/future_impl.dart 208:18 handleValue\\ndart-sdk/lib/async/future_impl.dart 932:44 handleValueCallback\\ndart-sdk/lib/async/future_impl.dart 961:13 _propagateToListeners\\ndart-sdk/lib/async/future_impl.dart 535:9 \\ndart-sdk/lib/async/zone.dart 1525:13 _rootRun\\ndart-sdk/lib/async/zone.dart 1422:19 run\\ndart-sdk/lib/async/zone.dart 1321:7 runGuarded\\ndart-sdk/lib/async/zone.dart 1362:23 callback\\ndart-sdk/lib/async/schedule_microtask.dart 40:11 _microtaskLoop\\ndart-sdk/lib/async/schedule_microtask.dart 49:5 _startMicrotaskLoop\\ndart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 186:7 \\n\\nThe test description was:\\n end to end extensions flow\\n═════════════════════════════════════════════════════════════════\\n\"}"]}
Failure Details:
Failure in method: end to end extensions flow
══╡ EXCEPTION CAUGHT BY FLUTTER TEST FRAMEWORK ╞═════════════════
The following RPCError was thrown running a test:
ext.flutter.inspector.structuredErrors: (-32603) Unexpected DWDS
error for callServiceExtension: WipError -32000 Promise was
collected

When the exception was thrown, this was the stack:
dart-sdk/lib/_internal/js_dev_runtime/patch/core_patch.dart 748:28 get current
packages/vm_service/src/snapshot_graph.dart.js 1870:41 new
packages/vm_service/src/snapshot_graph.dart.js 2530:23
packages/vm_service/src/snapshot_graph.dart.js 2538:76 [_call]
packages/vm_service/src/snapshot_graph.dart.js 2476:27 callServiceExtension
packages/devtools_app_shared/src/service/service_extension_manager.dart.js 1042:91
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 622:19
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 647:23
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 541:3 _asyncStartSync
packages/devtools_app_shared/src/service/service_extension_manager.dart.js 1049:40 call
packages/devtools_app_shared/src/service/service_extension_manager.dart.js 1084:62
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 622:19
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 647:23
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 541:3 _asyncStartSync
packages/devtools_app_shared/src/service/service_extension_manager.dart.js 1157:30 callExtension
packages/devtools_app_shared/src/service/service_extension_manager.dart.js 1186:51
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 622:19
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 647:23
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 593:31
dart-sdk/lib/async/zone.dart 1538:47 _rootRunUnary
dart-sdk/lib/async/zone.dart 1429:19 runUnary
dart-sdk/lib/async/future_impl.dart 208:18 handleValue
dart-sdk/lib/async/future_impl.dart 932:44 handleValueCallback
dart-sdk/lib/async/future_impl.dart 961:13 _propagateToListeners
dart-sdk/lib/async/future_impl.dart 535:9
dart-sdk/lib/async/zone.dart 1525:13 _rootRun
dart-sdk/lib/async/zone.dart 1422:19 run
dart-sdk/lib/async/zone.dart [1321](https://github.com/flutter/devtools/actions/runs/12798927680/job/35683997493#step:4:1322):7 runGuarded
dart-sdk/lib/async/zone.dart 1362:23 callback
dart-sdk/lib/async/schedule_microtask.dart 40:11 _microtaskLoop
dart-sdk/lib/async/schedule_microtask.dart 49:5 _startMicrotaskLoop
dart-sdk/lib/_internal/js_dev_runtime/patch/async_patch.dart 186:7

The test description was:
end to end extensions flow
```

Start by running the DevTools integration test containing the “end to end extensions flow” case and compare its output with the linked CI failure. Trace the DWDS error through the reported service_extension_manager.dart.js and vm_service snapshot_graph.dart.js stack entries; done means the integration test completes without the “Promise was collected” error.

Written by the indexing model from the issue text.