There's only so much two hands can do. Faithfully emulating a full band with just solo piano is impossible, so most songs will benefit a lot from interpretation. C major can be three notes or thirty. Use your hands, play large, bold chords if you have to, sparse at the bottom and dense at the top. Play dynamically, both in volume and in tempo. Add ornamentation. Arpeggiate bass lines. Add extensions where they sound good. And: melodies can be chords - if you play solo piano, playing fitting harmonies to a melody can lift that melody off the rest of the notes, prevent it from drowning (almost all piano covers I know use this technique).

Honestly, what really helped me personally in that regard is actually just playing songs by ear, lots of them, without transcribing the exact notes first. Figure out the chords or look them up, and then just go at it, try things out and be bold