For a moment there, I also got my hopes up and thought that it addresses my other gripe, but not quite. :-(
If I flag a message in MacOS Mail, webmail will correctly star it, so that's good. And if I unstar a message, it gets unflagged on the server correctly, so that's good too. But if I star a message in webmail, this special status only appears in webmail, when it should later appear as a flag in Mail. Not sure where the error is here. Oh well.