Function screen_area_and_average_cached_z3_scheduled 

pub fn screen_area_and_average_cached_z3_scheduled(
    vertices: [(i16, i16); 3],
    depths: [u16; 3],
) -> (i32, u16)

Run hardware-safe NCLIP and AVSZ3 for an already-projected indexed triangle.

The cached screen coordinates and depths are loaded together. The three SZ writes occupy part of the silicon-required NCLIP result gap, so callers that need both winding and an OT key avoid paying two independent GTE schedules. The returned area is identical to screen_area, and the depth is identical to average_cached_z3 with the installed ZSF3.