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To be able to transfer the products to another organization you need to be org admin for both of the organizations, so the button will work.
The message is informing that you are not an org admin for the destination org, so even if you are a site admin and administrator of the instance, you can't transfer if you are not an org admin.
Once you have the correct access, you will see the same information as below:
You need to ask the org admin to add you to this new organization for you to transfer the products.