In some cases, Roman numerals aren't all that helpful, and this piece might be one of them.
In my opinion, Section A is best understood by considering two simultaneous actions:
- The chromatic descent in the bass from E, through E♭ and D, to the tonic D♭.
- And the constant presence of the tonic D♭ in all four of the chords. The D♭ is obviously the root of D♭, it's the 6 of E6 (spelled as C♯), the 7 of E♭7, and the maj7 (again spelled as C♯) of Dmaj7.
These two aspects make it very clear that D♭ is tonic, and that's ultimately what drives the harmonic motion: tension and resolution to that D♭.
The B Section is less clear, but there are two things to consider: B Sections often go somewhere else tonally, and here it seems to be rooted in A, which is enharmonic to ♭VI (B♭♭), a relatively common move dating back almost two centuries. Note also that the overall tonic D♭ is still present in every single chord, though now always spelled as C♯: it's the third of Amaj7, the sixth of E6, and the fifth of F♯add9.
In other words, Coldplay makes clear what the tonic is by playing it in every single chord of the song. If you try to sing a D♭ throughout the song, you'll see that it fits everywhere!