Do I need to file anything with the tax office?

No, you will not be required to file any documents related to the account transfer with the German tax office. 

In case you are an Austrian client, the transfer to the new Scalable must be reported to the Austrian tax office within 1 month after the transfer. Otherwise, the transfer may be treated as a deemed sale, which could result in capital gains tax of 27.5% on unrealised gains. Scalable Capital will provide a report in your Mailbox approximately two weeks after the transfer to support you with the tax filing via FinanzOnline. Scalable Capital does not provide tax advice. Please check the Austrian Website for more details.