I may be late to this conversation.
May not help you but just my thoughts in case this happens to someone else.
I have had to purge sour chickens crops before. Although not ideal, I think I would have tried to push the latch side back out of the birds mouth and extract the whole zip tie, instead of clipping the end and hoping for the rest to pass through the digestive tract (with a potentially sharp clipped end).
Also, cleaning the hole is (obviously) a good idea. It wasn’t mentioned but I would try liquid bandaid or superglue to hold it closed and hope it healed. Surface lacerations to birds tend to heal more successfully and quickly than one would suspect.

hoping for the best for your bird.