Threads new ‘Supplemental Privacy Policy’ (Instagram link) says they’ll collect (from fediverse users interacting with Threads users):

• Username
• Profile Picture
• IP Address
• Name of Third Party Service
• Posts from profile
• Post interactions (Follow, Like, Reshare, Mentions)

From the linked article:

“Granted, these sound like basic table stakes for federation to work well within the Fediverse. Most Mastodon servers collect roughly about the same amount of data for basic features to work correctly. But again, Meta is first and foremost an advertising and data harvesting company…”