Apparently, as I feared it might happen, it's linked to your Instagram account.

I've seen notifications in Instagram saying "Your friend X just posted for the first time in Threads" this is JUST what I did not want, to have both things linked, my Twitter is silly I don't want my family or old friends to follow me there.

Conversely, semi-public figures like journalists or CS researchers might not want people to follow them on Threads so that people don't immediately find their Instagram account (I believe you can still keep that private and have to manually approve followers, though).