IF my understanding is correct, you can actually keep a denormalized version of user information (name, shipping info etc) and still be compliant, assuming you do not use that billing information for any purpose other than billing.
The "right to erasure" isn't as strict as the "right to be forgotten" -- You (the end-user) would need to prove that merely having your name and address in billing records violates your right to privacy. And to make that argument you'd have to provide evidence the business is using said information for purposes other than billing.
Personal data can be used lawfully to "fulfill contractual obligations with a data subject" (eg: fulfilling a purchase, and retaining information for warranty/returns/RMA etc purposes) and "To perform tasks at the request of a data subject who is in the process of entering into a contract with the controller.
" and "For the legitimate interests of a data controller or a third party"
The "right to erasure" isn't as strict as the "right to be forgotten" -- You (the end-user) would need to prove that merely having your name and address in billing records violates your right to privacy. And to make that argument you'd have to provide evidence the business is using said information for purposes other than billing.
Personal data can be used lawfully to "fulfill contractual obligations with a data subject" (eg: fulfilling a purchase, and retaining information for warranty/returns/RMA etc purposes) and "To perform tasks at the request of a data subject who is in the process of entering into a contract with the controller. " and "For the legitimate interests of a data controller or a third party"