Kit Marlowe may have been a spy, but no way they could be the same writer. The style and concerns are completely different. Besides Marlowe’s peak was while Shakespeare was still developing and Marlowe died before Shakespear’s best work.
Don’t remember the details now, but Shakespeare did plagiarize Marlowe. I wrote a term paper on it over fifty years ago and at the time it took some digging, but the proof was there. Don’t get me wrong, I love Shakespeare and Marlowe as well. Who knows how great he could have been.