Is always so hard mode trying clean up after a villianess you reincarnate into. Much as growing up is hard, better to be reborn than putting out fires from someone else's gender reveal party.
"Rent boy" seems correct. I mean, it's British but that doesn't mean it's wrong. From the chat screenshot, it seems that someone doesn't know that it's a real term. Rent boy is the cheap kind of male prostitute. The more expensive kind is called a male escort or gigolo. All these terms include the "paid for" or "whore" connotation while "boy toy" could just be a younger boyfriend.
the maid didn't say the person is dead, so perhaps it's related to that player girl. It fits with the common trope seen in chinese emperor harem stories, a concubine "hangs" or "killed" herself but it was only an "attempt." It's just some ploy to garner sympathy. I'm betting it's either the player gal or some else such that the player could sneak into the MC's room while everyone is checking out the servant that tried to hang themselves.
otherwise I don't really see how the player is going to be able to investigate the MC's room for her quest.