Update an existing product as a vendor.

Image URLs already stored for the product, or repeated within the request,
are ignored after trimming whitespace. Existing images retain their ordering
and mirrored local files; images_added counts only newly inserted images.
Explicit image removal happens before deduplication, so
remove_existing_images: true can replace images using the same URLs.

For bulk or shopify sources, sync_images: true reconciles the complete URL
array: retained images keep their IDs and local copies, missing images and
stored duplicates are removed, and the first image becomes primary. An empty
array clears the gallery. A missing or null array is rejected. Do not combine
reconciliation with explicit removal options. images_synced: true confirms
successful reconciliation.

A category or category_id that cannot be resolved, or that names a category
Oyster does not carry (hair care, makeup, fragrance, supplements, tools & devices,
baby, grooming), is declined: the product keeps its current category and the rest
of the edit is saved.