[js/web] use the recommended workaround for Vite (#23531)
### Description
After some investigation and debug, I decided to follow the recommended
workaround as suggested in https://github.com/vitejs/vite/issues/8427.
### Motivation and Context
There is a known issue with Vite 5.x when using WebAssembly package.
Detail information is in https://github.com/vitejs/vite/issues/8427.
There are previous attempts to fix this problem (#23487). I tried
various ways to make it working out of the box for Vite users but none
of them worked: Some "fixes" did fix the usage of Vite but broke other
use case/bundler and some introduced other issues. Eventually I figured
out that there is no good way to fix this inside ONNX Runtime.
Considering the root cause is inside Vite and it may be fixed in Vite
v6. I think now the best way is to follow the recommended workaround.
