[Python] Remove AWS SDK bundling when building wheels

### Describe the enhancement requested

In #12227 we decided to use a bundled version of the AWS SDK when compiling Python wheels, in order to downgrade the AWS SDK version.

Now that we have fixed S3 finalization issues (#36442), it should be ok to rely on the vcpkg-installed version of the AWS SDK again.

### Component(s)

Packaging, Python