Since you didn't specify and I don't know enough about Threads to say with certainty I'll assume you're logged in. At that point that's all that matters. Posting will only associate whatever you say with your account but ultimately your posting isn't exactly what they care about, they can monitor your traffic and usage in a number of other ways, especially if logged in.
That's not entirely how this works though. I mean you aren't wrong, but it's not fully automatic (anymore). At least as far as I know.
They can't necessarily association your phone with you if you don't choose to provide them with access to your tracking ID. That was the default in the past, but isn't anymore. Facebook was really really pissed about Apple making this a user choice.
Additional they can only track you within your browser if you signed in with a Meta/Facebook account on one of their services. But yes. If you do that every site that contains something from Facebook (Login with Facebook, a post, some other thingy from Facebook) will report back to Facebook that you've visited them.
This all being said: Facebook is the worst if it comes to this stuff.
Edit: we were talking about the Threads so here right? You are totally correct if over just used the browser or a PC.
Yep. These details are true too. I was over simplifying for the sake of argueing, “yes it’s possible.” As an end user who doesn’t understand the nuances here, one would find no reason not to just say yes to everything.