Please check that your Google account is connected to the game, and that it is connected to PlayGames.

Here are some steps worth trying:

-Make sure to update Play Services, Play Games and/or Play Store
-Clear cache, storage and data from these apps
-Go on Play Games or Play Store, log out of your account and try to log in again directly from the game.

If you go to the Play Games settings, you should find a "Change account for games section". In this section, there is an option to "Change account by game" in which you should be able to select Little Nightmares and it will open a window. If the window indicates "Signed out" under the title Little Nightmares, this might be the problem.

You can then select the address with which you used to be signed in and the synchronization might work again!