vet.sh: linting does not work for pull requests

While looking at the https://github.com/googleapis/google-cloud-go/pull/9758 it seems that linting is actually not working for modules. For example, copying locks should have definitely triggered a CI failure, which it did not.

Most go tools work in a single module boundary and should be executed at every root of `go.mod`. So, either the script or workflow needs fixing. From github actions output it would probably nice if every single module ended up as a separate result to make the distinction clearer. This probably can even be scoped, such that only changes in a particular module are linted.

Similarly, `golang.org/x/lint/golint` is deprecated and should be replaced with `go vet`. See the notice on https://pkg.go.dev/golang.org/x/lint.

The fix for making linting work again is trivial, but it needs a coordinated effort to get all the submodules passing the checks.