High pitch whine sound when cold starting

Recently had my starter replaced due to vehicle not starting and troubleshooting indicated the starter being the problem. After the new starter was installed, I started hearing a high pitched whine after my Tracer turned over. It lasted several seconds than shut off. It only happened after a cold start.
While removing the new starter (replacement is covered under warranty), noticed several damaged teeth on the flywheel. Now my problem is which caused the damage to the other?
I just had my transmission rebuilt a month ago and a flywheel inspection is part of that job. I have been using the same shop (known the same owner as well) for 15+ years without any problems. He states that any damage should have been noticed by his mechanics.

Since the starter problem got above my ability, I took it to a local shop to check out. They texted the damaged teeth after the new starter was whining. They are just looking at it as a new job costing $1,000.00 (parts and labor). So, no one noticed any damage to the flywheel before the starter was replaced.

My problem (and question) is this. There was no whine before the starter was replaced. So, is it more likely that the starter Bendix gear caused damage to the flywheel (perhaps not disengaging like it was supposed to) or is it the damaged flywheel causing damage to the starter? I have no real experience in this area because I have never had this problem before. I would appreciate someone, an unbiased third party else s opinion and reasons.