[Steely Tom]

Maybe I’m seeing things, but that airplane looks like it could become an actual fighter plane with the addition of weapons.

I’m referring specifically to the full-area control surfaces on the tail. These make it suitable for supersonic flight, correct?

[NorthMountain]

It's supposed to replace the T-38 Talon, which is supersonic ... that's the whole point. It's a supersonic trainer for pilots who will transition to supersonic fighters.

[BatGuano]

Well, not so sure that the “full area control surfaces on the tail” are necessary for supersonic flight but it looks more like the F-16 than the F-16 itself.
I flew an airplane in the Ohio ANG, the F-84F, that was “supersonic.” The limiting Mach was 1.1...and achieved in a dive. The airplane had full area horizontal stabilizers but really a fighter-bomber, not an air superiority fighter like the F-15.