Hmmm from the way she shocked by knowing the mother is esemori high school friend there is several points that can be pointed out
1. The mother knows esemori personally. I don't know how close, but from the way the idol shocked i bet the mother knows the secret about esemori past.
2. It could be that the mother is the girl that survive from lovers abyss and then the boy who died is esemori relatives or close one.
3. If esemori is a trans, i bet esemori would not use the same name before he trans. Since the mother fastly recognized esemori one she sees him, i guess her mother familiar with his looks since past (so probably not trans).
4. Or it could be that the info about esemori being trans and keeping the name the same spread in this town fastly so it could be that once the mother hear esemori name she remembered esemori suicide lover and being a girl in the past.
Regardless all of that, i thought they would be having sex tho, but sensei sex curse giving the MC some tied down chain. Though the body of the idol is so hot on this