This HII based News Release “HII Breaks Ground On New Submarine Facility At Newport News Shipbuilding” of Feb 9, 2023, is significant in that the USN is part funding a Multi-Class Submarine Production Facility with no reference to the AUKUS SSN pact's existence.
This strongly indicates the only major submarine builders in the US (HII, but also GD EB) are not seen as major designer/builders of the AUKUS SSN hull.
It is therefore likely the AUKUS-Australian SSN hull design/build oversight role will fall to the UK, specifically into BAE's SSN(R), by default.
Furthermore the first design contract has been awarded for the UK's PWR3 reactor to go into the SSN(R) hull.