[Copilot]

Description

Optimize the WebGPU SparsePagedAttention execution pipeline:

• write directly to the activation output for single-source attention without a head sink, avoiding FP32 partial-state allocation and the finalize dispatch
• compute online-softmax scalar state once per workgroup and share it across lanes
• run finalization with one workgroup per (token, head) and share merge coefficients across output dimensions
• keep staged joint-softmax finalization for main-plus-auxiliary attention and head-sink configurations
• account for the updated workgroup-memory requirements and preserve shader-cache specialization
• add focused auxiliary direct-output coverage and update the WebGPU operator documentation

This follows #32533, which is now merged into main.

Motivation and Context

The original WebGPU implementation always materialized FP32 partial softmax state and launched a separate finalize pass. It also repeated per-head scalar calculations across output lanes. These changes reduce scratch-buffer traffic and dispatch overhead for the common single-source path while reducing redundant work in staged configurations without changing attention semantics.

Validation:

• WGSL template tests: 89 passed
• clang-format --dry-run --Werror on the changed C++ files
• git diff --check
• focused code review found no correctness, synchronization, bounds, or numerical issues