I went ahead and looked into a help page about UPS optional coverage here as well:

File a claim with UPS

Amazon’s Buy Shipping service enables you to access shipping solutions offered by a network of shipping carriers, including UPS. When you use Buy Shipping and related services from UPS, you must file claims of loss or damage directly with UPS regardless of whether UPS charges a Buy Shipping service fees to your Amazon account or linked UPS shipper account. Amazon may not file claims on your behalf or reimburse you for any successful claims. Upon successful resolution of a claim, UPS will reimburse you directly to the extent such payments are required by UPS terms and conditions.

To file a claim with UPS follow these steps:

File a claim with UPS by calling 1-800-711-5914

The UPS personnel at the above phone number are trained to support claims requested by Amazon sellers.

When submitting the claim, inform UPS that you are filing a claim for a damaged or lost item for Amazon seller-fulfilled.

If UPS will not move forward with your claim request or the claim was initiated but not paid, follow these steps:

Call UPS at 1-800-711-5914 (this phone number is designated for Amazon sellers), and request UPS to help with your claim.

If UPS continues to refuse to settle the claim, you can contact Amazon. However, before contacting Amazon, you must obtain the following information from UPS by calling 1-800-711-5914:

UPS tracking information (required)

First and last name, or agent ID, for the UPS employee who refused to initiate the claim (required)

Your contact email, phone number, or both–this will be provided to UPS (required)

Business name and full mailing address to where the claims payment check should be sent (required)

UPS claim number (if available)