No, the Aeotec Range Extender Zi is not directly compatible with the Bosch Smart Home system. Bosch only supports third-party Zigbee devices such as this range extender via special integrations such as Home Connect Plus or Home Assistant, not natively. The in-house data and product data sheets do not list Bosch compatibility.
I also don't understand why these things have to be plugged into a socket. Any cheap USB power supply would be sufficient for 1 watt and the manufacturer would save a few cents on electronics, space and, above all, the expensive certifications for low voltage.
Unfortunately, we cannot guarantee compatibility. Therefore, the question has been forwarded to our Community so that experienced users can share their knowledge with you.