[web] In profile mode, user code crash causes diagnostics crash

When DiagnosticsNode is used in profile mode it crashed during FlutterErrorDetails construction.
Fix PR : https://github.com/flutter/flutter/pull/53878

## Steps to Reproduce

throw exception in a build function when using flutter run --profile mode.
Look at stack trace, instead of showing user code it crashes in diagnostics.
