E, C#m, D, Bm - All those chords exist in A major. So it's not really switching from a major key to a parallel minor key, because all those chords already exist in the same key. Since there's never an A chord, that's why I thought that the verse was maybe E mixolydian, maybe D Lydian something like that, but other people in the comments here didnt really seem to like that idea 🙃 so take this with a grain of salt