I Became a Vicious Supporting Actress (2021)

FL is an aspiring series script screenwriter While napping, she is transported into her own story, becoming the Third Princess Chen Qian Qian, a side character, killed off in the third episode by the male lead, Prince Han Shuo. Armed with the knowledge of her own script, Xiao Qian is determined to stay alive and find her way back home.

Modern day woman ends up in novel.
Mini series with a novelist end up in a book and falling in love.Whiles trying to return home.

the same plot but the era is different

Along the lines of being from another time and going back and being an odd one.
The female lead seems to have various reasons to be around the male lead even after come from another time still falls for the male lead from this time line.
So I think they are similar in that stances.