I've done some research on this.
Around June 2023 at the time they merged account management with Google, FitBit updated the FitBit App. Since this update the syncing has only been one way. Blaze->App. Notifications still work though, it's only settings. This means that any chances you make on your App will never make it back to the Blaze. This sucks, because you can't set the date and time manually on the FitBit Blaze, so once the time is out of date it's essentially useless.
FitBit have denied any wrongdoing and are simply stating that the Blaze is an out of warranty item. Any tickets you log will eventually direct you to their store page to buy a new watch.
I look after my items. I've got a pristine condition FitBit Blaze that is useless. I'll never buy a FitBit item again. I've already sworn never to buy a Google WearOS watch again after Google did the same thing with the Moto 360 Sport watch. I advise you to ditch FitBit and go to either Apple or Garmin as these manufacturers offer support for a long time.
EDIT: A bit more research on this and my findings are unbelievable!
I unpaired my Blaze from my Pixel 6 Pro and paired it to an iPhone 12 on my daughter's FitBit account. It works 100%. Everything syncs fine in both directions. The time and date syncs and I can change the clock face.
I unpaired it from the iPhone and back to the Pixel 6 Pro and it doesn't sync. The time is obviously correct now, but changing the time zone doesn't work and I can't change the clock face so it's not syncing from the App to the Blaze again.
Other than the OS, the difference between the two configurations is the auth method. On the Android phone I've migrated my account to Google and on the iPhone the account is still a FitBit account.
The end result is:
Googles own ecosphere doesn't work. Google Android using Google's FitBit and Google auth will not sync with the FitBit Blaze
Apple's iOS using Google's FitBit with the original FitBit auth will sync with the FitBit Blaze.
This is entirely on Google and FitBit and it's something they can fix if they want to, because it's already working on iOS. A junior tech at the could confirm this is the case if they cared about their customers.
