I can't help you with talking to Etsy's customer service. We are all sellers here just trying to help other sellers.
After years of neglect, Etsy has finally realised if an identical product photo is available on multiple sites, it makes Etsy look like just another Amazon, Ebay, AliExpress. The result was buyers leaving the site en masse and Etsy's "handmade" reputation in tatters, especially when buyers discovered their $70 item is available elsewhere for $15. Ask buyers why they shop "handmade" on Etsy it is to buy something really unique and unusual. They also pay a premium to buy directly from the creative/designer. The problem grew so large Etsy couldn't enforce the new "creativity standard" relying on pattern matching bots and user reports. Unfortunately there has been a wave of "false positive" reports. The message to sellers is be more vigilant of your intellectual property being used elsewhere.
If I was in your situation I would:
- sweep all the sites I found your images on an document your efforts to remove those images
- ask your production partner for an exclusivity agreement in your contract if they are using your design
- have a range exclusive to Etsy
- have a very discrete watermark to prove the design, and the photos, are yours in the future
- take new photos of your current range
I know the suggestions will be both expensive and time consuming but it can be written off. I'm going to assume your production partner sends you finished product samples so you can check the ongoing quality of their work and protect your customer base. If you are working with a "minimum order quantity" - common with most manufacturers - finished samples are usually part of the process. You can also take your own photos using those samples and sell it direct when that item is ordered.
I'm sorry. It's a gut punch to find your work being copied and/or mass produced without your permission.
