Is there any airport which has a precision instrument approach using only GNSS (augmented with LAAS) for guidance?
The FAA has an FAQ on GBAS (ground-based augmentation of GPS/GNSS). It says they no longer use the term LAAS, instead they now use GBAS to be consistent with ICAO terminology. A GBAS approach is called GLS on the approach charts.
The FAQ has information about where GBAS is used:
Where are operational GBAS systems located?
Currently, two U.S. locations have obtained operational approval for public GBAS use and support revenue airline traffic. These stations are located at Newark Liberty International Airport (EWR) and Houston George Bush Intercontinental Airport (IAH). Internationally, several airports have GBAS and support revenue operations (Bremen and Frankfurt, Germany; Sydney, Australia; Malaga, Spain; Zurich, Switzerland; and 15 Russian locations).
Newark (KEWR) has 5 GLS approaches, Houston (KIAH) has 6. I looked at a couple of the approach plates and they didn't require any additional equipment apart from the GBAS equipment itself. Note that GBAS is not the same as the 'typical' GPS/WAAS combination used for RNAV GPS approaches, and it requires different equipment:
Can the same avionics be used for GBAS and WAAS?
The GBAS and WAAS standards are different and initial avionics and integrations only supported one of the two capabilities. Emerging aircraft integrations can support both services (e.g. A350).