Where does the robot's camera data go?

That depends on the system and is one of the most important questions to check before procurement.

Many systems transmit telemetry, diagnostic or image data to the manufacturer's servers. If these are located outside the EU, the rules on transfers to third countries apply. For countries without an adequacy decision, the effort involved is considerable.

Ask specifically: which data is transmitted, to which provider, at which location, who has administrative access, and is there a data processing agreement? A general assurance about the server location is not sufficient for this check.

The most effective lever against this is operation without an external connection.