You can think of this as a Mary Sue, but I don't think this is a Mary Sue.
If Mary Sue is just an original character who falls in love with one of the characters from the original show, then this is definitely a Mary Sue - although I have reservations about whether they are in love.
If the essence of Mary Sue is that everything is to satisfy the premise of letting the self-created character shine, then this one is obviously not it.
I just want to write about the impact that every encounter in life may have on me under the vast starry sky (what) and in the boring world (cough). A new encounter, a new possibility, an... Inexplicable entry point (hey hey).
But the truth is - I just wanted to write the story of a terrible woman and a terrible man (beat).
So if you feel uncomfortable, please turn around and go out. If you are still willing to read on, then I would like to say thank you in advance.