In this situation, are you required to stop and wait until the pedestrian has completely crossed to the other side of the road?

Why?

The visible traffic island separates the traffic streams, so the crossing sections on either side count as separate crossings. You do not have to wait for the pedestrian to leave the section beyond the island, outside your path. You must still take extra care and give way to anyone on or entering the crossing directly ahead of you.

art. 13 ust. 8 i art. 26 ust. 1 Prawa o ruchu drogowym