Thank you for your reply! I did check the Magento logs, but there were no errors. BUT, your comment helped me realize that the problem could be the OAuth interface between VSF and Magento.
To test this theory I set “Magento / Integrations / Resource Access” to “All”. Now all the products are in stock again! Then I reset the permissions based on the installation instructions to see if maybe some new permissions might have been added recently to set only the permissions that are necessary. After doing that, it still works.
So, either the docs have been updated recently with one or more new permissions or somehow I missed checking the box on one or more permissions when I set up the integration. (Probably the latter.) Regardless, the problem is solved. Thank you very much for your help!