Wands have a certain loyalty to those who have wielded them. Any wand but the Elder Wand will possess at least some degree of attachment to its previous owner, merely because of their time wielding it, as indicated in this answer. Given that Harry had wielded his wand for seven years, it probably was fairly attached to him.
In addition, phoenix-feather wands are choosy about about whom they allow to wield them.
According to Pottermore:
Phoenix feather wands are always the pickiest when it comes to
potential owners, for the creature from which they are taken is one of
the most independent and detached in the world. These wands are the
hardest to tame and to personalise, and their allegiance is usually
While Harry may have been imbued with certain qualities from the presence of Voldemort's soul, the majority of his personality was diametrically opposed to that of Voldemort. As mentioned here, we don't really know exactly why Harry's wand picked him. It probably had something to do with Voldemort's connection to him, but it may not have. For example, perhaps the feather was inclined to choose wizards with great innate power, which both Harry and Voldemort possessed.
From the same Pottermore source, of unicorn-hair wands:
They are the most faithful of all wands, and usually remain strongly
attached to their first owner, irrespective of whether he or she was
an accomplished witch or wizard.
This seems to indicate that other wands care about how powerful a witch or wizard is, which would have been a good reason to choose Harry or Voldemort.
In any case, if Harry's personal qualities influenced the wand to choose him, those still existed after the part of Voldemort within him was destroyed.