How do I get my refund from Dyson?

I purchased a Dyson Airwrap on January 29, 2025 and it was delivered on February 4, 2025. Unfortunately the Airwrap arrived damaged so I requested to send it back. I was told by Dyson customer service that they can help me with an exchange but it would take 18 business days for the exchange to take place. I opted to return the damaged Dyson and order a new one. Dyson provided me with a reference number and was told to take the machine to a UPS store and they would wrap the machine and print the label for me. I returned the defective Airwrap on February 7, 2025 and tracking shows that the Airwrap was delivered and signed for by Dyson on February 11, 2025 at 10:17am. I contacted Dyson to inquire about my refund but they stated that there is no record of the machine in their warehouse. I was told that my issue was escalated. I never heard anything back from Dyson so I filed a dispute with my bank. Dyson is now telling me that I need to file a claim with UPS. I went to the UPS store today and the UPS associate submitted a customer claim/investigation. She told me that the machine was delivered but UPS will investigate and get the GPS coordinates to show that the package was indeed delivered to Dyson. I called Dyson upon leaving the UPS store and spoke to Carlos. Carlos stated that I need to go back to UPS and file a claim in which I did. Carlos then told me that I need to cancel my dispute in order to get a refund. I called my bank and they told me if I cancel the dispute then it cannot be reopened and the dispute will go in the merchants favor. Should I cancel the dispute? My fear is that I cancel the dispute and Dyson will not issue me a refund. I don’t know what I do. I know I sent back the machine and it shows it was delivered to Dyson. I just want Dyson to do the right thing and to issue my refund. I am currently out $649.49. Any advice and assistance would be greatly appreciated.