New VSCode fallback behaviour for copyToClipboard (#6598)

Adds a fallback behaviour for copying which will allow copy buttons to actually work in VSCode.
NOTE: success toasts will no longer show in VSCode though.
I've also added some logging just in case a user is looking at their console when a copy fails. Hopefully this provides enough information that the unhide-able error doesn't look suspicious.

Related to https://github.com/Dart-Code/Dart-Code/pull/4814
Fixes https://github.com/flutter/devtools/issues/5775
Mirror package:web version from Flutter SDK