[WebGPU] Fix stale buffer bindings on first graph-capture replay

[hariharans29]

Lazily create the graph-mode BufferManager and gate routing through it on a graph_buffer_mgr_active_ flag set only between OnRunStart/OnRunEnd. Refactor GpuBufferAllocator to take a std::function<const BufferManager&()> getter so the allocator can resolve the active buffer manager dynamically.

Pre-existing latent bug: when graph capture is enabled, captured commands held buffer pointers from the capture run. If the allocator freed and reused a slot before the first Replay(), the dispatch read stale memory and produced one wrong logits tensor. Mostly hidden in fixed-shape decode because the allocator typically re-handed out the same addresses; exposed by MatMulNBits MLP/QKV fusions which churn the allocation pattern (#28280)

Also adds WebGpuContext::WaitForQueueIdle() and ComputeContextBase::FlushAndWait() helpers used by the buffer-mgr lifetime management.

Motivation and Context

Fix correctness on first replay

[Copilot]

Pull request overview

This PR addresses a WebGPU graph-capture correctness issue where the first replay could read stale buffer bindings. It does this by routing allocations through a dedicated “graph-mode” BufferManager only during the capture window, and by letting the allocator resolve the currently-active buffer manager dynamically.

Changes:

• Lazily create the graph-mode BufferManager and gate WebGpuExecutionProvider::BufferManager() via a new graph_buffer_mgr_active_ flag (active only between OnRunStart/OnRunEnd).
• Refactor GpuBufferAllocator to optionally take a std::function<const BufferManager&()> getter, enabling dynamic buffer-manager selection.
• Add WebGpuContext::WaitForQueueIdle() (implementation) and a ComputeContextBase::FlushAndWait() convenience helper.

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
onnxruntime/core/providers/webgpu/webgpu_execution_provider.h	Adds graph_buffer_mgr_active_ flag to control graph buffer manager routing.
onnxruntime/core/providers/webgpu/webgpu_execution_provider.cc	Lazily instantiates graph buffer manager, toggles active flag during capture, and updates allocator creation to use a getter.
onnxruntime/core/providers/webgpu/webgpu_context.cc	Implements WebGpuContext::WaitForQueueIdle().
onnxruntime/core/providers/webgpu/compute_context.h	Adds FlushAndWait() helper and expands BufferManagerAccessor friendship.
onnxruntime/core/providers/webgpu/allocator.h	Adds <functional> and a new allocator constructor taking a buffer-manager getter; stores the getter.
onnxruntime/core/providers/webgpu/allocator.cc	Implements new constructor and switches alloc/free to use the getter.

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