> another point to make it safer would be sharing the "chat" with the lawyer, this way it becomes media of communication.

This guy made the same argument, but as the court detailed, this is a misunderstanding of attorney-client privilege. Sharing an unprivileged conversation with your lawyer doesn't make it privileged. A phone call to your lawyer is privileged, but a phone call to your cousin Jimbo about what you should tell your lawyer is not.