It doesn’t have a “season 2” (as mentioned above it is a game and didn’t get an anime adaptation) Although there is an OVA
As for the sequel there is one. Danganronpa 3: The End of Hope's Peak High School nowu will find that is has a Future Arc and the Despair Arc.
If I remember correctly it’s the Despair Arc first as those events happen before the Future Arc. Also just an FYI but don’t worry, u don’t need to play the game to understand what’s happening in the “3rd Season”