Will Breathedge 2 have base building at launch?

No: the developer currently places personal bases and planetary building in a later major update.

The short answer

The developer explicitly warned players waiting only for base building that it is not part of the initial Early Access release. Personal bases, separate structures, and planetary gameplay are planned for the second major update.

What you can do at launch

Launch descriptions do confirm crafting, equipment upgrades, repairing and dismantling machinery, resource gathering, exploration, and survival systems. None of those statements should be stretched into a claim that free-form base construction is already available.