Why does aircraft stability increase when it transitions from subsonic to supersonic flight?
Static longitudinal stability (also called static margin) is determined by the distance between the center of gravity and the neutral point¹. The neutral point is at a quarter of the chord at subsonic speed and moves back to half chord once the aircraft flies fully supersonically. This means that the static margin will greatly increase when moving from sub- to supersonic flight.

In order to keep the center of pressure at the center of gravity, in supersonic flight the elevator needs to create lots of downforce. The bigger the difference in lift per area between wing and elevator, the stronger pitch stability will become.

This effect makes the transition between both regimes tricky: When accelerating, aircraft experience the shift in the center of pressure as Mach tuck, and when the trim facilities are not sufficient, the aircraft might enter an uncontrollable dive.

In the reverse direction, an aircraft trimmed for supersonic flight will experience a pitch-up moment from the forward shift in the center of pressure once it slows down, which can stall it or overload the structure.

¹ I could also talk of the center of pressure here, but that would be less precise. The neutral point is the center of pressure for all angle-of-attack-dependent lift forces, and it is those which determine pitch stability.