[CI][Tune] Remove duplicate new Tune output CI pipeline

[hongpeng-guo]

Why are these changes needed?

We have a duplicate CI pipeline for the new output engine, even though it's already enabled by default. There's no need for the duplicate pipeline. This PR removes the repeated CI pipeline.

Related issue number

Closes #44775

Checks

• I've signed off every commit(by using the -s flag, i.e., git commit -s) in this PR.
• I've run scripts/format.sh to lint the changes in this PR.
• I've included any doc changes needed for https://docs.ray.io/en/master/.
  • I've added any new APIs to the API Reference. For example, if I added a
    method in Tune, I've added it in doc/source/tune/api/ under the
    corresponding .rst file.
• I've made sure the tests are passing. Note that there might be a few flaky tests, see the recent failures at https://flakey-tests.ray.io/
• Testing Strategy
  • Unit tests
  • Release tests
  • This PR is not tested :(

[hongpeng-guo]

Please let me know how to unit test buidkite changes. Thx! :)

[justinvyu]

@hongpeng-guo Take a look at buildkite/premerge -> Details, then make sure you don't see the tune new output tests being run anywhere.

[hongpeng-guo]

@hongpeng-guo Take a look at buildkite/premerge -> Details, then make sure you don't see the tune new output tests being run anywhere.

@justinvyu Just double checked and confirmed that tune new output tests was removed in buildkite/premerge :)

[justinvyu]

Thanks for cleaning this up!