[Core] ray.init(logging_format) argument is ignored

[kevin85421]

Why are these changes needed?

#32741 accidentally removes the logging_format parameter from the setup_logging function. This PR overwrites the formatters for all default handlers.

Related issue number

Closes #44713

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 :(

[jjyao]

Code lgtm, let's add a test so we don't have regression in the future.

[kevin85421]

Code lgtm, let's add a test so we don't have regression in the future.

Add a test 82e1018.