It is unclear

As you've noted, the class description states that they are monk weapons, which are inherently different from unarmed strikes. But when you put the build together, the attack information does state they are unarmed strikes.

Because of that, Wizards have contradicted themselves a bit, but I'd lean towards the class description vs what fields they put in for the build. But you and your DM may decide otherwise.

It's still playtest

Try it out! If you or your DM wants to use them as unarmed strikes in addition to being monk weapons and either of you feel it is overpowered, then you can decide not to count them as such.