If your vendor is using Etsy, you can use Jetti to publish and automatically sync products. Tracking details can be entered by the vendor through a vendor portal, as Etsy doesn't currently allow orders to be synced.
To sync with SquareSpace, under the Order sync options select Email / vendor portal. Then, connect a new inventory feed. You'll just need to the username for the vendor. No additional authentication details are required.
You might also want to enable the Allocate inventory button. As Jetti doesn't sync orders with Etsy, this will reduce the inventory levels for items sold while the vendor is yet to confirm and shipped the items. This is useful to prevent over selling. Once items are shipped, vendors should reduce the inventory quantity within Etsy.