I love how sloppily the Shinigami filled out that form. "Don't worry about it." "Almost died, but managed to miraculously stay alive. Happens all the time. Trust me." There's a 100% chance the Shinigami is going to get caught in the future, and then we'll get to meet her boss or some meddling co-worker. She better hope that they like yuri too, or she's going to get in trouble.
The Shinigami is basically a stand in for the audience. A yuri enjoyer. Silently watching, until corrective action is needed to get the yuri back on track. The ultimate wing-man.