This PR updates the dartdoc version to v6.2.2.

Release notes:  https://github.com/dart-lang/dartdoc/releases/tag/v6.2.2

The main impact for Flutter is to update dartdoc to add chips to class and/or mixin pages for class modifiers.  See dart-lang/dartdoc#3391, dart-lang/dartdoc#3402.   This will also be a cherry-pick candidate for 3.1 if it can land in time.

- [ test-exempt ] I added new tests to check the change I am making, or this PR is [test-exempt].