[web] a few updates to web pipeline (#17485)
### Description
Update the Web CI pipelines:
- remove parameter 'WebTemplate': Since we start to support webgpu, the
linux-web-ci.yml is no longer working and it is already out-of-date.
remove this file and parameter so that we always use win-web-ci.yml
- change flag `RunWebGpuTests` into 2 flags, for release and debug.
Currently for CI we only run webgpu tests on release build. But we want
to have the capability to run webgpu tests on debug build as well.
After this PR is merged, next step is to enable both Debug and Release
webgpu tests in PostMerge pipeline.
