This prelude is a pastoral and while it could be described as very broadly binary in form the two themes are in D major and A major, with the second theme ending in such a way as to lead into the fugue as a kind of developmental interruption.
The movement is scored as "Andante" but if I were to try to describe this prelude it would be as a Koshkinesque take on the Adagietto from Mahler’s Fifth Symphony, weird as that is likely to sound to fans of either Mahler or Koshkin or possibly to fans of both. That's just the kind of mood this prelude suggests to me. Others will, naturally, have a different set of impressions.
The first theme is in D major and moves in a slow and pastoral way. While all the phrases are in simple two-measure building blocks the first two larger phrases are six measures each before settling into more persistently duple patterns across the phrases. I identify Theme 1 as spanning the entirety of measures 1-11 with the transition to Theme 2 starting at 12 (0:42). In my earlier analysis I located the transition later on in the prelude. Measure 11 is now where I regard Theme 1 as ending, with a Neapolitan harmony that deceptively resolves to B minor.
Koshkin sets up an Andalusian cadence descent at 0:42. Rather than complete the descending I, VII, VI, V of the cadence Koshkin pivots so that the G chord at measure 13resolves not to F# as we’d expect but to a second inversion B flat chord. He continues to destabilize the tonality of the phrases until he gets to Theme 2, in A major (1:27)
Theme 2starts at 24 and is gentle and quiet. In fact I might dare say that Theme 2 is more like a repeating cadential riff that could have been the ending of Theme 1 that has been postponed by an extended modulating transition to not appear until it has functionally become a Theme 2 in a sonata exposition. The pulsing accompaniment hasn't changed but the melody is written out in half note values, making it seem more restrained and subdued than even the opening theme. It's a simple motto of C#, F#, F natural and E, transposed up an octave in the second phrase (measures 26-28) This is very nearly simple a cadential formula presented as a secondary theme, which in many respects it is, but it accomplishes an A major chord that prepares for what's coming next.
The fugue subject is not necessarily related to the initial theme of the prelude. At first glance you can see that the whole thing is scored in a single voice and ask whether or not this thing is even a fugue. It is, it's just that the subject and associated material is so staccato it makes sense to score it as a single voice rather than attempted to flood staves with notational indicators of how each of the lines in the fugue need to be delineated. If this were scored for string quartet, by contrast, highlighting the separate melodic lines would be easier.
The subject is a four on the floor quasi-blues riff and the subject and respective answers are presented no less than five times. It sounds to me as though the fugue subject, with its ambiguous scale degrees, continues the material of Theme 2 from the tonic key—what could have been a slow, pastoral sonata has been cut off at the end of its exposition to make way for a wiry and impudent five-voiced fugue.
presentation 1 is in the tonic at 0:00
presentation 2 is in the dominant at 0:08
presentation 3 is in the tonic at 0:14
presentation 4 is in the dominant at 0:21
presentation 5 is in the tonic at 0:28
Once you recognize the subject you can hear the five presentations of it in the spritely exposition. With a subject this springy and short we unsurprisingly have just a few middle entries. The first middle entry shows up in C sharp minor at 0:41 (measure 59). After another episode the second middle entry appears at 0:59 (measure 69) but it's ambiguous. If you were to merely look at the score and the linear patterns you could see the fugue subject appears in F major but there's a preliminary appearance of D natural in the bass strings at the end of measure 68. I would say this recontextualizes the entire middle entry as really being in D minor.
At 1:14 (measure 76 Koshkin introduces a flurry of sixteenth note arpeggios that rise up aggressively six measures into a two chord pedal point at measure 82 (1:28) that prepares for the formal return of the subject in D major, which happens after a dramatic pause at measure 83 (1:33). This gentle piano climax lets the subject wind down still further into a half-cadence which resolves itself at measure 91 (1:58) into a recapitulation of the opening measures of the prelude. The fugue can be thought of as an eruption of energy intervening as an interlude between what could be thought of as the B section and the reprised A section of a truncated ternary form. The opening two measures are brought back with the melody in the trebles and then in the bass strings before coming to pianissimo close.