Here is the Threads Supplemental Privacy Policy referenced in the article. Some relevant excerpts are:
We collect information about the Third Party Services and Third Party Users who interact with Threads. If you interact with Threads through a Third Party Service (such as by following Threads users, interacting with Threads content, or by allowing Threads users to follow you or interact with your content), we collect information about your third-party account and profile (such as your username, profile picture, IP address, and the name of the Third Party Service on which you are registered), your content (such as when you allow Threads users to follow, like, reshare, or have mentions in your posts), and your interactions (such as when you follow, like, reshare, or have mentions in Threads posts).
And further down…
If you are a Third Party User, our ability to verify your request may be limited and we may be unable to process your request. Please note, however, that the interoperable protocol allows Third Party Services to automatically send Threads requests for deletion of individual posts when those posts are deleted on the Third Party Service. We make reasonable efforts to honor such requests when we receive them. Contact your Third Party Service to learn more.