How can I generate a report of all HS codes for my products?

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That is available in inventory export

https://help.shopify.com/en/manual/products/inventory/inventory-csv#:~:text=The%20HS%20Code%20(Harmonized%20System%20Code)

For automation you can script a solution using usemechanic to export custom CSV’s; useful if you have some complicated system or business logic you need to apply to get specific sets of codes or do validation. https://tasks.mechanic.dev/?q=export

Contact me with detail for pricing this type of solution.

Or you can use spreadsheet apps matrixfy or ez-exporter

https://www.highviewapps.com/blog/export-customs-information-data-from-your-shopify-store-with-ez-exporter/

https://matrixify.app/tutorials/update-shopify-product-hs-code-and-country-of-origin-in-bulk/