Currently the (non-web) Dart plugin registration catches exceptions and logs, but then re-throws. This means that if there's an exception in one plugin, all plugins that come after it alphabetically won't have their Dart registration run. This is a Dart version of the issue we already had and fixed with Java registration, which caused a lot of confusion before we changed it to catch exceptions.

We should keep the logging and remove the rethrow, so that only the problematic plugin will be broken, not other plugins.