Thanks, Ira. I ended up going to Messages Prefs on my Mac and unchecking "enable messages in iCloud" and that took care of it!
That's interesting and I'm glad it worked for you because on my Mac in Messages>Preferences I do not have any settings related to iCloud that I can turn off (or on).
MacBook Pro - M2, Ventura 13.6 Safari Tech Prev 17.0 Safari 16.6 Firefox 116.0.2 iPhone 7 Version 15.8
