Junkyouju Takatsuki Akira no Suisatsu (2021)

Both of them have supernatural powers and uses them to conquer something. The protagonists has flashback of their past too.

Both of them include supernatural elements. The main lead has some sort of power like how Naoya has a power. He is recruited as an assistant to a mysterious guy and they work together to solve problems.

Both shows feature university professors who, with the help of their students, investigate and solve folklore-related crimes or mysteries

Both have supernatural concepts. (While Junkyouju Takatsuki Akira no Suisatsu is all about folklore and mystery, Boku wa Doko kara is not all about it). In both, shows, one of the main leads has possessed an ability through which they help the other main lead to solve cases. The bromance is strong in both of them, and they eventually grow closer and understand each other as the story progresses.

light detectives with two main characters one of whom obsessed with investigations, and the other needs simple human peace of mind

I recommend this both drama because , Male lead and Female lead
try to solve problem
In one drama explosion and another student murder/suicide

Two best friends (one of them being a university professor) investigate and solve supernatural happenings