Updates a supplier branch saved in Zuper: its name, the job account used for orders, whether it is active, and whether it is the favorite (default) branch. Only the fields listed in the body schema are applied; other branch fields (address, email, delivery method, payment term) are validated but ignored, and the job account is not re-checked with the supplier. favorite_supplier_vendor defaults to false, so omitting it clears the favorite flag on this branch; sending true clears it on every other saved branch of the same supplier type. Deactivating the favorite branch, or setting favorite_supplier_vendor: false when no other branch of that supplier type is favorite, fails with 409. Admin only: the API key must belong to an admin user; other roles receive 405 Access Denied. The provider must exist and be CONNECTED; otherwise the request fails with 404 (unknown provider) or 403 (not connected or reconnect required).