So... is Romantic Killer finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: October 27, 2022
Manga finished: June 02, 2020
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Romantic Killer follows Anzu Hoshino, a high school girl perfectly content with her life of video games, chocolate, and her cat. She has absolutely no interest in romance, much to the dismay of a magical being named Riri.
Riri, believing Anzu needs a romantic life, forces her into a real-life dating sim scenario. He takes away her beloved comforts and throws various handsome boys her way, all in an attempt to make her fall in love.
Anzu, fiercely independent and determined to maintain her single status, resists Riri's efforts. She actively tries to avoid romantic entanglements, but the increasingly absurd situations Riri creates make it a constant struggle to stick to her principles.
The anime explores Anzu's hilarious attempts to thwart Riri's plans and navigate the unexpected arrival of potential love interests, all while desperately clinging to her beloved hobbies.