Do fly-by-wire fighter aircraft automatically reverse the direction of control surface deflections during a tailslide?
While the reversal of flight controls does happen, it is transient in nature, and in virtually all cases if you let the aircraft "fly" itself it will pitch down and recover.

Only aircraft with thrust to weight ratio of at least 1 to 1, and thrust vectoring of some sort if a jet, will be able to maintain the nose high attitude.

Prop aircraft are a different story as they essentially "hang" from the prop if the engine can develop enough power to do that.

Recovering from a tail slide is not like recovering from a stall or spin, you can't really use flight controls for anything until the aircraft develops enough airspeed for them to be effective, and in 100% of the times I have been in one, by that time the relative wind is normal and not reversed.

The exception is in prop aircraft where the prop wash against the rudder and elevator does provide some control effectiveness, but not reversed.