Migrate integration test suite to use elasticsearch-clients-tests

[JoshMock]

With elasticsearch-clients-tests now including filters to separate stack from serverless tests, migrating this repo away from the rest-api-spec tests in the Elasticsearch repo will create a more stable and maintainable—and thus more useful and not as easily ignored—integration test suite to run on PRs in this repo.

Tasks

Beta Give feedback

1. extract the integration test runner in elasticsearch-serverless-js into a separate repo (or just pick one repo for it to live in)
2. refactor test runner to take command line args to filter for the needed subset of tests, skip filters, etc.
3. ensure test runner can support a provided stack version (see Updates in STACK_VERSION for report elasticsearch-clients-tests#87)
4. update serverless and stack client repos and all CI jobs to use the new runner