Will game Groups sync between consoles?

So you have the cloud saves that will be through the XBox cloud service, then you have the saves that are located on your local Series X hard drive. If you can move the saves to the external drive youll have those avail. If the cloud automatically syncs the game save it will be from the cloud. Sometimes a game will give the option of what save via date and time you want to use. Just depends on the game and not sure if this one does it.

Hello Victor, sorry to hear you're having trouble with your controller.

If you'd like to set up a repair for the console or controller you can do so via https://account.microsoft.com/devices. However, if you let me know the issue you're having perhaps I can help resolve it.

I did not mean to ask whether the save was synced between cloud versions on different devices. What I meant to ask if whether the save could be synced between the cloud version and the locally installed console version.

At a time one controller can be synced only to one console/PC. But you can always switch between the devices by syncing the controller each time with the new device.

Your multiplayer progress is synced between the systems, not the single player campaign. Battlefield 4 has the same capability. None of the games support syncing progress of single player campaigns between systems.