Following up as promised @flavio-b, I heard back from the products team on the mechanics.
With multiple NS-PID barcodes, one per variant is all that’s needed. When a variant has several, there’s no deterministic rule for which one gets used, so I’d remove the extras rather than rely on any particular order.
I also need to refine part of my last reply based on the product team’s explanation. A Custom-typed barcode that holds a valid GTIN (correct format and check digit) is already used as the S-PID. Merchants shouldn’t tick “Has no standardized identifier” for those variants, because the checkbox declares that no standardized identifier exists. The safer move is to change those barcodes’ type to GTIN, UPC, EAN or ISBN rather than rely on Shopify inferring it, and the productVariantsBulkUpdate route I mentioned earlier works for that. The checkbox is only for variants whose barcodes are SKUs, internal codes, or other values that aren’t valid GTINs.
The declaration itself is meant to reach customs paperwork and carriers, including Managed Markets orders - that part isn’t live just yet, but keep an eye out.