AMD Warranty doesn't cover bent or broken pins on a processor.
Even though the CPU Cooler may have been defective but the moment you tried to remove the CPU Cooler and the Processor came out and was damaged is considered to be "Customer Error" thus the Warranty is voided.
In my opinion it is considered to be Customer Error because there are ways to remove the CPU Cooler that are stuck to the processor without damaging it. Since the processor wasn't damaged when you installed it but after you tried to remove the CPU Cooler causing the processor's pins to be bent thus it was your fault for not being more careful in removing a stuck CPU Cooler from the processor. AMD specifically states that Broken or Bent Pins are not covered by AMD Warranty.
If the pins are not too badly bent, there are many YouTube videos that shows you how to properly unbend the pins without breaking them.
Don't feel bad, this has happened to many other Users when they tried to remove the CPU Cooler and ended up damaging the Processor.
But if you still want to try and open a AMD Warranty Request here is the correct link: https://www.amd.com/en/support/kb/warranty-information/rma-form
This AMD Warranty link explains what is covered and what isn't concerning AMD Processors: https://www.amd.com/en/support/kb/warranty-information/pib