In the fourth and sixth measures (shown above) how should the brackets be interpreted? Should all subsequent notes in the treble clef with stems pointing downward be played with the left hand? Or only the specific bracketed chords?
Suggestions regarding which fingers or which hand to use are just that - suggestions. A pianist should use whichever helps produce the desired sound. Try the various possibilities and see which works for you. In bar 6 you may even like to try using 2 and 3 for the bracketed notes and continuing the left hand for the next 3 notes before using the right thumb for the E (marked 2). There are no hard and fast rules, except that it should sound right.
It coud have easily been written out so the middle section notes appeared in the bass clef. That would eliminate the need for any bracketry. However, as with any new piece, fingering is personal, and just one of the myriad of 'things to consider' when exploring a new piece. The correct way to play it is so that it sounds authentic, and that's up to the player. There's more than one way to skin a cat. So I'm told...