
Quick answer — Sayuri performed 2 anime themes, including "Mikazuki" from Rampo Kitan: Game of Laplace, "Tsuki to Hanataba" from Fate/EXTRA Last Encore.
Sayuri performed the anime theme songs "Mikazuki" (Rampo Kitan: Game of Laplace), "Tsuki to Hanataba" (Fate/EXTRA Last Encore).
Sayuri's first listed anime theme is "Mikazuki", the ending of Rampo Kitan: Game of Laplace.