In X-Cart Marketplace, with enabled content moderation for the new vendor-created product pages via the Trusted/Non-Trusted Vendors add-on, vendors without a "Trusted vendor" status have to submit all new products they create for approval to the store administrator. The store administrator reviews each new product and either approves or declines its publication in the product catalog. The vendor submitting a product can track its publication status (sent for approval, approved, declined). They can also search/filter their products by the publication status.
Find out how a vendor without the "Trusted vendor" status can:
Submit their new products for approval by the storefront operator/store administrator. See Getting New Products Approved for Publishing
Find out the publication status of a product. See Finding out the Publication Status of a Product