The Threads team is addressing one of the biggest initial user concerns with the app – users now can delete their Threads profile independent of their existence on Instagram.
There is now a new option in your Threads settings under "Account"/"Delete or Deactivate Profile," allowing you to deactivate your Threads profile. And if you don't reactivate it within the next 30 days, it will be deleted completely and won't affect your Instagram profile due to any change in it.

Initially, because Threads sits on top of the Instagram infrastructure, your Threads and IG profiles were inherently linked: your Threads profile was actually a sub-element of your IG presence, rather than being distinct.

That freaked out some users, who hadn't wanted to lose their Instagram account but were in the grey area with Threads. Instagram committed to fix this, and now they have-it's separated the two, allowing much more control over each.

While you can't have a Threads profile unless you have some kind of presence on IG, so they're still linked in one key way. But now you are able to get rid of your Threads presence without having to also cull your Instagram identity.

This is a good move and good update. And as Threads continues to grow, it's going to seem bound to become even more independent of IG. Though apparently that isn't going to happen when it comes to DMs.

Another recent exchange on Threads had Mosseri also clearly state that DMs are not currently on the horizon for Threads.
But such a link could still be created between your Threads profile and your IG DMs, which, in turn, would have to see them linked with your Messenger and WhatsApp inboxes, too, by implication. Yet that doesn't seem very high on the agenda for the Threads team at present, judging by Mosseri's comments.

So, mixed results for Threads users. Now, you can delete your Threads profile, but not separate DMs for the foreseeable future.