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I think it means how you interacted with the characters, but each of their deaths was only kind of your fault, since Monika was the one who did the most damage. Like, you were the one who persisted in trying to get their endings, so Monika is kind of blaming you? I don't know.

The weird part is I got this message after I booted the game up and only Sayori had died at that point

Yeah, same here.