Hello,
WoodMart uses its own Brand attribute instead of the default WooCommerce Product Brands taxonomy, which is why the brands from WooCommerce are not appearing in product feeds and styles.
Unfortunately, there is no built-in way to automatically link both taxonomies. If you want to use Woodmart brands, You need to change core brands permalinks from “brands” to something like “core-brands” in Settings > Permalinks.
But if you want to use a new core brand instead of the theme’s custom attribute, need to deselect the custom attribute in Theme Settings > Shop > Brands.
Best Regards,