[webgpu] refactor a few "context" classes #7655

Job	Run time
precheck	1m 40s
wasm_Release_static_library / build-wasm	7m 1s
wasm_Debug / build-wasm	37m 18s
wasm_Release / build-wasm	56m 42s
web_Debug / build_onnxruntime_web	18m 21s
web_Release / build_onnxruntime_web	23m 26s
	2h 24m 28s

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