We talked about mediants in Mitski's song "When Memories Snow." What other songs use mediants?

Oh! Darling - The Beatles (Paul McCartney)

         D                  F7
When you told me you didn't need me anymore
          A
Well, you know I nearly broke down and cried
         B7
When you told me you didn't need me anymore
          E7            F7            E7             E7#5
Well, you know I nearly fell down and die -ie -ie-ie-ied

The song is in the key of A, and the transition from verse to chorus has A-A7, which naturally leads to D with A7 being a dominant of D. We then jump up a minor third to F, which provides some tension and floatiness, and then jump up a major third back to the tonic. The bass walks up stepwise to A too, outlining a "Mario cadence."

We then have a v/v secondary dominant leading to the dominant chord E, but move up a semitone to F again and then back down to E. This movement by semitone has a similar feel to the phrygian I-bII-I movement. The F is still a mediant compared to A but feels phrygian-y in this context. Shows how the same chord can feel different based on the chords surrounding it.

Froot - Marina and the Diamonds (Marina Diamandis)

 
G
Come and fill your cup up
Bb               A
Looking for some good luck
G          Bb           A
Good luck, good luck to you
G
Hanging like a fro-oot
Bb           A
Ready to be ju-uiced
Eb
Ju-uiced, ju-u-u-uiced
 
          Gm
Living la dolce vita

(The chord progression in the pre-chorus is the same as in the first half of the verse)

We have a pretty unusual chord progression here with G jumping up a minor third to Bb and then planing back down to Bb. The movement is between 3 roots that are ultimately stepwise from each other (G-A-Bb). Then from the A we have a tritone jump to Eb, which is a chord in Gminor, the parallel minor of G.

This is mostly planing around three chords near each other, but starting with a jump up a third, which is always slightly unsettling.

Hypno K.K. - Kazumi Tokata

This charming short song from Animal Crossing shows how unsettling the mediant can be. The piece starts by simply swinging back and forth between C and Ab. The title of the song shows that the aim is a hypnotic effect, which I think the movement from tonic to submediant demonstrates.

https://musescore.com/user/14115336/scores/6681201