Since the money is passing through your personal bank account it is your turnover.
Things might be different if the account was a business account owned by the property owner and if you were an employee. But that is not the case.
See an accountant if you need reliable advice. I run a business but am not an accountant, not a tax adviser.
Having reviewed relevant EU legislation, the answer, though surprising, seems to be:
Place of Supply of Service is Germany (place where the painted wall is located), according to article 45 of Council Directive 2006/112/EC. Thus applicable rate is German rate payable to German authorities.
There is no small business exemption, despite this being a one-off ...
Which VAT rate is applicable and how do I pay it to which country?
German - you provide services locally and physically in germany. You need to register with the german VAT authorities for that.
There are exceptions if you run a quite small invoice you STILL invoice it in Austria. There is basically a limit per year per country under which you can use your ...