Tone curve
The tone curve is a graph that lets you control your photo's brightness per tonal region: shadows, midtones and highlights separately. Dragging points up or down makes those tones lighter or darker. It's the most powerful contrast tool you have.
The classic S-curve, highlights up a little and shadows down a little, gives contrast with far more control than the contrast slider. Lift the bottom-left point and you get that matte film look with lifted blacks. Work calmly: small moves have a big effect. Besides the regular curve you can often work per color channel (red, green, blue) for color casts and color grading.
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The presets on this site set these adjustments up for you as a starting point, which you then fine-tune to taste.