Found this summary of
GM engines.
I would guess the new H3 engine would be something like the LH6. The old 5.7L referred to above is most likely the Gen II LT1, so this is 2 generations more advanced.
"LH6
An improved LH6 version with Displacement on Demand will push output even higher. It is a Generation IV small-block and features the improvements found on other Gen4 motors. An early batch of fifty 2005 Saab 9-7X SUVs for the Canada market used this engine with the Displacement on Demand feature disabled.
LH6 applications:
2005 Chevrolet TrailBlazer EXT/GMC Envoy XL SUVs
2005 GMC Envoy XUV
2005 Buick Rainier (without Displacement on Demand)
2005 Saab 9-7X
An automotive version of the 5300 V8 will also be offered in the Pontiac Grand Prix in 2005."
I looked up the Envoy specs. The V8 gets 300 hp and 330 lb ft of torque. It gets EPA mileage of 15/19, as opposed to 15/21 for it's V6.