all I know about axis theory is that it has to do with transposing chords across minor thirds, which is something I do. tbh I mostly wrote the harmony on intuition. I can give some random thoughts
the opening chords are built on two sets of minor sixths, the left hand moving up a minor third and the right hand moving down a semitone.
I view m. 10 and m. 45-48 as extended V-I's (Db to Gb). the extensions leave us only a glimpse of the dominant-tonic relationship, which gives the sense of a lost innocence or something of that nature
as for the the messiaen-like section at m. 22, it's grounded in pedal points cycling in major thirds (E, C, Ab). The section concludes with the Ab pedal tone, which acts as a iv chord to Eb minor. (and in modulating to Eb minor, the right hand plays B-D#-A#, and then plays D-F#-C#, so there's more of those minor-third shenanigans). The "bell" chords in the high registers of the piano have a few recurring elements. oftentimes there is a chord in the left hand which is played simultanenously an octave or two up, only moved down a semitone, creating a major-seventh dissonance in every single note. (example: m. 22, Eb minor over E minor). I often use Minor-major seven chords, augmented major seven chords, minor major sevens with a raised fifth, and minor major sevenths with a flat fifth. so in m.33-34, I constructed the chords as a G# minor-maj7 sharp 5 with an Eb melody on top; G minor-major7 sharp 5 with a Db melody on top; and B minor-maj7 sharp 5 with an F# beneath, respectively.
you may also notice a couple occurrences of chords with a two major thirds separated by a major-seventh interval. (example: m. 54, C E B D#).
another note on m. 53-54. I constructed this as another one of those "uncanny-valley" V-I's, being G to C. The G chord is: G, F, Bb, Eb, Ab, and the C is the aforementioned: C, E, B, D#. However these two chords are interrupted by another chord: Bb, Gb, D, F. so calling it a V-I is an even bigger stretch. however that intercepting chord was constructed as being a Gb augmented major-seventh chord, which is a tritone away from C, so I guess there's more of that axis-theory stuff.
the ending sets up a V-I to Eb minor: Bb, D, Ab, C#. and then B, D, Ab, Bb, which I saw as a Bb dominant chord with a b natural in the base. Then the base jumps down F, and the D, Ab, and Bb are repurposed as the natural sixth, minor third, and fourth of an F minor chord, which "resolves" to the final extended C minor chord.
there's also a few sus shapes in this piece. I'm particularly a fan of this, i guess it's a major-add4 chord in second inversion. for example, in m. 38 on the third beat, the right hand plays a sus 2 shape: Eb, F, Bb, while a D plays in the base, creating this particular chord.
I also realized there's a type in m. 31 on the second beat, the left hand says E and G when it should be C and E.