But Meta's head, Adam Mosseri, said DMs aren't in the development pipeline for Threads.

Initially, Meta was so hesitant to add messaging features to the new app, but now, Threads' team apparently appears to be working on an in-stream DM option, which gets it closer still to X and other social apps.
From data privacy researcher Jorge Caballero, new to the Threads app has been some fresh data strings appearing to be related to DMs.

Caballero says threads' DMs are likely end-to-end encrypted while users can also send self-destructing messages, if they so choose.

Which is pretty much in line with Meta's other messaging tools, while the fact that it's looking to add encryption by default would also enable it to be inter-operative with Meta's other messaging features, in line with its broader messaging integration plan.

Which may also have been part of the reasons why the Threads team was not keen on adding messaging to the app in the first place. Meta has been working on integrating all its messaging tools since 2019, which will eventually merge all your DMs-Messenger, Instagram Direct, and WhatsApp-into a single, interoperable inbox, accessible in any app.

In short, all your messages across each one of the apps would be viewable across any platform, and thus you could message somebody on WhatsApp from IG, send a Messenger DM to a person on WhatsApp, etc.

And so, given this, Meta wants to keep its DMs within its existing systems, because adding yet another inbox into the mix likely complicates things quite a bit. And as it strives to become a bigger competitor for Twitter/X, in order to encourage broader usage, DMs remain much-requested - and so Threads needs to add DMs to tick all the boxes.

Though there's been no official confirmation as yet. As noted, Instagram chief Adam Mosseri has seemed fairly hesitant on the DM front, though his wording around such has softened in recent weeks.

So it now seems likely that this is coming, which will make a lot of Threads converts happy, especially as it looks to capitalize on its recent momentum, in the wake of X's more recent updates.
Indeed, after X changed the link previews format, and with reports of rampant misinformation and fake reports around the Israel-Hamas war, and as conversations are increasingly dominated by the platform's small percentage of paying users, Threads has seen a respective increase, according to fresh data published on Tuesday by data.ai, data.ai reported.

As Platformer's Casey Newton noted:

Between Saturday and Wednesday [this week], Threads rose from #40 to #20 on download charts. The biggest impact was felt in the UK, where it rose 32 places from #92 to #61 overall."".

So far, no official word from Meta, but it does seem that there was a bigger shift to Threads, amid continuing concern over the direction of Elon Musk's X project.

Whether this translates to more usage shift, we will soon see. Till then, it seems like Threads does build up and adding DMs along with edits, Trending Topics, audio recording, etc. In total, maybe Threads will become a real challenger for the original bird app.

The DMs would surely chime in here. Keep watching this space for further development.