As @Howlium says, the legato applies only to the "melody line" in the top voice of the left hand, not to the staccato chords. As for execution...
EDIT: It's significant that the chords in measure 32, from the beginning of beat 2 until the "grace-chord" on 4, all lack staccato markings.
In addition to the legato melody over staccato chords, there are particular problems in the left hand's tied D4 on m. 32 beats 2-3, and the tied C4 in m. 33, beats 1-2.
In Alexander Kobrin's performance on YouTube, you can watch his hands in this section. The relevant portion is from 1:40 - 1:49. The entire LH "singing" line is executed by Kobrin with an accented staccato articulation, using the sustain pedal to create the legato. Note that in the case of D4, he re-executes it on beat 3, but he does not re-execute the C4 in the following measure.
There is also a "synthesiafied" Richter performance. The color-bars in mm. 32-34 suggest two possibilities:
- That his hands are big enough, for example, in m. 32 to play the beat 2 chord with his thumb on D4, then cross fingers 2 and 3 over the thumb to execute the chord on the half-beat. This technique would work for the remainder of the passage, excepting m. 33 beat 2.
- On the D4, there are slight breaks in the color-bar, so perhaps he's actually re-articulating the note very quietly. (Pretty unbelievable feat, IMO, and less likely, but it's Richter.)
He does seem to use very light sustain pedal in that passage, though not so much in the piece as a whole.
Giving this passage a try (but short of performance speed), I would most likely execute it by changing the pedal just after I play each melody note. So, for example:
Beat 2: play all four notes with pedal, but near immediately release the pedal and all notes but D4, then reapply pedal to catch D4 (which I would continue to hold with my thumb).
Beat 2&: play chord with 5-1-2, releasing the pedal, but again holding onto the D4 and immediately reapplying the pedal.
Beat 3: play the 2-note chord, then release all three keys, but keep the pedal until playing the chord on ...
Beat 3&: same technique of catching the melody note with the pedal applies here and after.
Beat 4: keep the pedal through the "grace chord", but change it upon playing the F4.
And so forth...