After the cutscene, follow Sebastian out of the catacomb and then speak to him when you have the chance. You'll have the option to learn Avada Kedavra, and then the Side Quest ends.

Hogwarts Legacy follows a young fifth-year ... where players can use each of the following Unforgivable Curses: Avada Kedavra, Crucio, Imperio, and the Blasting Curse, Confringo, with Unforgivable ...