Threads now has a Supplemental Privacy Policy (https://help.instagram.com/515230437301944) regarding their policies relating to "Third Party Services" like Mastodon. Should Threads interconnect with Mastodon via #ActivityPub, this addresses what they will do with our data.
Note that they will collect information about anyone "allowing Threads users to follow you or interact with your content". The information they collect will include your profile, your content, and your interactions.