Often, there are themes related to the power dynamics in their relationship. Since Kaguya has a certain status, the fanfic might explore how the reader fits into that world. Also, friendship turning into love is a popular theme. They start as friends or acquaintances, and then gradually, deeper feelings develop between the reader and Kaguya.
One common theme is unrequited love. The reader might be pining for Kaguya, or vice versa, and there's a lot of emotional turmoil as a result. Another theme is the exploration of Kaguya's character. Writers often delve into her personality, her insecurities, and how the reader can interact with and influence her.