The latest Ventura update fixed (at least for me) a problem of transferring two-factor authentication codes from text messages received by iMessage to Safari and other apps. Bravo!
The latest Ventura update, alas, also added a new bug, which is that the "new message" indicator stays on even after that TFA message has been read and deleted (especially on Macs).
I have an iMac (Intel), a Mac Air (Apple silicon) and a recent iPhone, all with up-to-date software.
The 'new message' icon (little red dot with a number) does go away on the iPhone when deleted elsewhere. But it is stubbornly persistent on both the iMac and the Mac Air. I have tried quitting the application; turning off notifications, quitting and turning on notifications in the Settings, to no avail. Rebooting the Mac Air did fix the issue -- it was there on reboot, but then vanished before I could even open the Messages app. Rebooting also fixed it when it stuck on the iPhone one time.
It's good to know that this spurious 'new message' indicator can be gotten rid of, but of course rebooting every time I get a text is not a viable solution in the long term.
I know those Apple engineers are mucking around with what is by now an absurdly complicated set of connections, communications, settings, etc.... so good luck, and keep working on it. Ventura is getting better with the updates. (It would be nice to fix the TouchID-switching-between-users bug on one of the next updates, too!)