Being such a new plane, wouldn't it have collision avoidance?
Yes, it would have TCAS.
However, TCAS hasn't prevented other mid air collisions. It isn't full proof.
Yes, but it's no guarantee. The aircraft that collided over Switzerland about four years ago both had TCAS, but the pilot of one followed the TCAS direction while the other followed the controller's contrary direction. (If a controller issues a command contrary to TCAS, the pilot is to follow the TCAS instruction and not the controller.)
In this case, it's possible the pilot ignored TCAS for whatever reason; it's also possible that the pilot of the bizjet (which may have TCAS but probably isn't required to) and the pilot of the 737 tried to "avoid" each other in the same direction and clipped.