In cases like this, the stem direction shows the hands: down-stem pitches are played by the left hand while up-stem pitches are played by the right hand.
The engraver had a few choices:
- Use the notation from the preceding two bars by changing the middle staff into treble clef.
- Use the notation from the preceding two bars by using an 8va marking (or something similar) in the middle staff.
- Or just do it as shown here.
You could potentially make a case for Choice 1, since the middle staff soon changes into treble clef anyway. But I think the given notation makes it very clear that it's a continuous musical line split between two hands that connect registrally.
Patterns in music crop up quite often. It would be weird to not follow the previous pattern, so yes: share the arpeggio between your hands.
The previous notation is used - it's just all put on one stave/staff. This is possibly because the notes are too high to be written on the bottom stave/staff with the bass clef; the amount of ledger lines would be too many and thus, not easily readable.
In order to show which hand plays which note, the composer has written the notes to be played with the left hand with the tails down and the notes to be played with the right hands with the tails up. The reason why this isn't done in the previous two bars is because they are able to utilise both staves, putting the left hand notes on the bottom stave/staff and the right hand notes on the top.
In the last two bars, what is the proposed way to play. Are you meant to switch hands?
Yes. This is quite obvious: the fact that there are no rests in the left hand in measure 5, the separation in measure 3 and 4 of your copy and the stem direction in measure 5 are absolutely unambiguous.
If so, why isn't the notation from the preceding two bars used?
You could also ask:
and why isn't the notation from the following bar (5) in the preceding two bars used?
the purpose was actually to avoid more than 2 ledger lines.
But you are right: the layout of the editor would be more logical and coherent if the stem direction of the right hand in bar 3 and 4 was the same as in bar 5.