It's because slats allow a higher Angle of Attack. They work by pointing the nose of the wing downwards so that at higher AoA there is no flow separation at the upper surface near the nose. Deflecting the slats does not increase $C_L$, the aeroplane must increase AoA to do that. Lower stall speed comes with the higher $C_{Lmax}$

From this answer, which also contains a graph showing that flaps increase $C_L$ at constant AoA.

It's because leading edge devices allow a higher Angle of Attack.

The four types of leading edge devices work by pointing the nose of the wing downwards so that at higher AoA there is no flow separation at the upper surface near the nose. Deflecting the slats does not increase $C_L$, the aeroplane must increase AoA to do that. Lower stall speed comes with the higher $C_{Lmax}$

From this answer, which also contains a graph showing that flaps increase $C_L$ at constant AoA.

It's because slats allow a higher Angle of Attack. The work as by pointing the nose of the wing downwards so that at higher AoA there is no flow separation at the upper surface near the nose. Deflecting the slats does not increase $C_L$, the aeroplane must increase AoA to do that. Lower stall speed comes with the higher $C_{Lmax}$

From this answer, which also contains a graph showing that flaps increase $C_L$ at constant AoA.

It's because slats allow a higher Angle of Attack. They work by pointing the nose of the wing downwards so that at higher AoA there is no flow separation at the upper surface near the nose. Deflecting the slats does not increase $C_L$, the aeroplane must increase AoA to do that. Lower stall speed comes with the higher $C_{Lmax}$

From this answer, which also contains a graph showing that flaps increase $C_L$ at constant AoA.