The
official answer is that having a receipt "helps" but "may not be necessary."
Costco can pull the purchase history on a membership, and it is said that receipts can also be displayed on the app.
If it is important, not a bad idea to electronically scan the paper receipts that are provided today anyway. They're thermally printed, and will fade over time, or deteriorate more rapidly when exposed to heat.
Or, some retailers, like Walmart and IKEA, offer electronic versions that can be downloaded.
A battery purchased prior to the switch from free replacement to prorated warranties in the middle of 2023 should be grandfathered under the old 36-month replacement warranty.