Dear Medjan, restarting worked like a charm and the Bats are back on the balance- thank you for your quick help!
Since the Bas were not transfered to wallet yet, a wallet back-up would not have helped, right? Just out of curiosity: Is there a recovery-option for bats that are not on the wallet yet but still in the browser?
So they are working on a full synchronization function. But I don’t know for sure what he means with “Brave Rewards data”. It could mean that you would loose your pending rewards when using the current wallet backup functionality. But again I’m not sure about that.