Facebook/Instagram has owned the domain for a while as they had a prior Threads app as far back as 2019, shut down in 2021.
https://techcrunch.com/2021/11/17/instagram-will-shut-down-i...
From WayBack, it looks like they bought the domain in 2010:
https://web.archive.org/web/20191001000000*/http://threads.n...