The answer is very simple. You should have a simple automated one-click method of knowing where all data relate to each user is, and an automated way of clearing it all. Job done.
Even with the tech, it still requires a human (for now) to read the request, understand it and process it.
Perhaps the future is AI interpreting the request and doing all the operations automatically or providing the client with a panel that can do all of these without having to contact the company.
The hard part is the right to be forgotten which requires the company to remove all information that pertains to a person. The tech stack still has to implement some stuff here in order to reduce costs and make it easier.
Having to contact your database administrator because you can't delete something without leaving dangling information all over is bad tech implementation which will probably require a huge rework for some companies.
I wonder how you can send the information to the client. If you use GMail then GMail will also know the personal information (they used to read your emails.. good stuff).