You have so many things mixed it.
This is a one-shot chapter used to promote the final Live Action movie. It gives some information new information on L, M, and N, but is ultimately pretty useless.
Death Note: Another Note is an unofficial prequel novel that focuses on Naomi Misora and L's case before Light picks up the Death Note.
The Shinigami people think was Light was the person in the Death Note special that aired on television after the anime finished its course. A recap of Light vs L, with a few new scenes such as Light on top of L's grave screaming at him.