In various places -- here, the bird app, even YouTube comments -- I keep running into people with some variation of the same question:
"Does Scum Villain have a teacher/student romance?" And every time I want to answer with: No, But Also Yes, But Also Not Really, It's Complicated (And That's On Purpose.)
Which is an answer that's too long to fit in a tweet or a YT comment, but fortunately tumblr has no (effective) post limit! So here I go.
In the very straight forward porn cliche sense of "oh but professor, I really ~need~ to pass this class or my life will be ruined, can't I do ~anything~ to get you to change my grade?" *bats lashes* and "Hoho, my pretty young teen student, I've got your good grade right here in my pants, if you ~apply~ yourself..." then no.
No sex or romance between a teacher and their student in the bounds of a teacher-student relationship happens in this book. No deliberate grooming of an underage student on the part of a teacher occurs in this book. No sex or a romance between an adult character and an underage character occurs in this book, nor is the adult 'waiting' for the minor to reach adulthood to initiate one.
No sex or romance between a teacher and their student in the bounds of that relationship happens in this book. Two people who were formerly in a teacher and student relationship do enter into a sexual and romantic relationship by the end of the book. Also the nature of the society they're in further means that even though they are no longer in the schooling environment, it is socially assumed that the deference owed by a student to their teacher lasts forever, even after the student leaves that environment, and they continue to regard themselves and refer to themselves in those roles even though the teacher no longer strictly speaking has authority over the student.
Also, the student was really hot for his teacher even when he was still a student. (The teacher was oblivious to this fact.)
By the time sex and romance is even on the horizon for these characters, their relationship has so drastically changed from that of a "teacher and student" that it is barely recognizeable as such. The power/authority dynamic between a teacher and their student is subsumed pretty much entirely by the facts that:
A. The 'student' has become a medeival fantasy warlord of such unsurpassable magic and might that literally no other person in this world can stand up against him, 'teacher' included, and the 'teacher' is well aware of that.
B. Also, the 'student' is metaphysically endowed (heh) with the Protagonist Halo, a literally active force within the setting they're part of, which means that not only can he not be defeated, he ontologically cannot be denied anything that he desires; what he wants, he gets, and what he doesn't want, cannot be forced on him.
C. ...But also, the teacher in this setting is a metaphysical outsider to the world order the student is part of, which means that he is aware of all of the above, and can and does manipulate it to suit his own agenda, which may or may not align with giving the student what he wants at any point in time. Assuming that the teacher has the correct understanding of what the student wants. (He doesn't.)
D. ........But also also, for all his power, one harsh word from him can destroy him. For all his knowledge, one tear can devastate him. (Which one? Both.)
4 - It's Complicated (On Purpose)
*throws the chalk against the wall*
Between a teacher and their student, who has the power? Between an emperor and a scholar, who has the power? Between a hero and the villain he is predestined to destroy, who has the power? Between a character and the reader who's read ahead to the end of the story, who has the power? Do we find some of these power imbalances more acceptable than others? And if so, why do we?
The Scum Villain's Self Saving System is a lot of things, but one thing that absolutely defines it is that it is a parody. It's a parody and a deconstruction of a lot of things -- the 'stallion' genre, the 'isekai' genre, the 'pay-per-chapter webnovel' genre, the 'gay drama' genre and, most relevant to this conversation, it is a deconstruction of teacher-student romance.
What kind of a teacher-student romance has a clueless, fish-out-of water NEET in the role of the Wise Old Mentor? What kind of a teacher-student romance has a black-hearted, demonic, domineering feudal warlord in the role of the Blushing Virginal Student? What kind of a teacher-student romance has the two principals so close in age -- by the end of the book, they may be as little as a year apart -- that they're more like peers than teacher and student? What kind of audience are we, going into a story like this one and finding ourselves cheering for the teacher to fall in love and lust with his student, only to be disappointed when that doesn't happen because the teacher fails for three books straight to recognize love and lust when it's literally looking him in the face and crying?
Asking "does Scum Villain have a teacher-student romance?" is sort of like asking "does Galaxy Quest have a lot of high science fiction concepts?" No, but also yes, but also not really. It's complicated, and that's on purpose.