Phantom unread messages in iMessage

After a (generally) successful migration from an old MBP (2014, Big Sur) to a new M2 MBA, I have several unread messages indicated by the notification badge in the dock on the iMessage icon. I've tried rebooting, logging out and back in, killall Dock, and even clicking on every single thread in the messages app, but nothing works. How do I get rid of the phantom messages? FWIW I don't have this issue on my phone connected to the same account.