[wasm] remove --vcpkg in wasm build (#24179)

### Description

There are slightly mismatch for the build flags for Web build pipeline
when using vcpkg.

A [fix](#24012) is on the
way but for now we need to disable vcpkg for the next patch release.

### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->

Author: fs-eire

tools/ci_build/github/azure-pipelines/templates/linux-wasm-ci.yml

@@ -51,7 +51,7 @@ jobs:
     os: linux
   variables:
     buildArch: x64
-    CommonBuildArgs: '--parallel --use_vcpkg --use_vcpkg_ms_internal_asset_cache --config ${{ parameters.BuildConfig }} --skip_submodule_sync --build_wasm --enable_wasm_simd --enable_wasm_threads ${{ parameters.ExtraBuildArgs }}'
+    CommonBuildArgs: '--parallel --config ${{ parameters.BuildConfig }} --skip_submodule_sync --build_wasm --enable_wasm_simd --enable_wasm_threads ${{ parameters.ExtraBuildArgs }}'
     runCodesignValidationInjection: false
     TODAY: $[format('{0:dd}{0:MM}{0:yyyy}', pipeline.startTime)]
     ORT_CACHE_DIR: $(Agent.TempDirectory)/ort_ccache