Apparently I am seeing an issue here in Big Sur with it (just updated to the latest beta too).. I have one chat in here, me and the misses, that is always on going. Its staying in sync between Mac and iPhone just fine. Nothing else on the desktop side is in sync with my phone. I was just messaging my mother on my phone earlier. Came in just now to check it, her last message to me on the Mac is the last time we spoke a month ago. The chat above hers was last updated 2 weeks ago, etc. Even after hitting 'Sync Now' in the prefs, its not updating. Going by the dates, it stopped when I upgraded to the Big Sur beta, but for some reason that one chat IS getting updated. The rest are chopped liver or something.