Record product→merchant-profile write path; refresh Current state

Document the now-functional product→profile write path in the payments
guide (set_product_merchant_profile, post-write pattern, picker gating,
double-Option clear). Mark the multi-profile GAP closed, drop the done
work-queue item, and note the discovered set_product_entitlements_catalog
rows_affected gap.

docs/guides/payments.md

@@ -39,6 +39,14 @@ merchant_profiles (1) ──< (N) payment_providers
 - **merchant_profile_rail_preferences** — tie-breaker `(profile, rail) → provider`
   when a profile has two providers serving the same rail.
 
+Products attach to a profile via `repo::set_product_merchant_profile` (validates
+the profile exists → 404, else UPDATE), called **post-write** from the create /
+update handlers — same pattern as the entitlements catalog. The admin product form
+renders the profile `<select>` only when >1 profile exists; a NULL
+`merchant_profile_id` resolves to the default profile (`merchant_profiles::for_product`,
+NOT the bare repo query, applies that fallback). On `UpdateProductReq` the field is a
+double-Option: `Some(None)` clears back to default-resolution.
+
 **Rails** are buyer-facing methods (`lightning`, `onchain`, `card`), declared per
 provider kind via `rails_for_kind` (BTCPay → lightning+onchain; Zaprite →
 card+lightning+onchain), NOT stored per row.