CI: Deduplicate linting checks
https://github.com/pandas-dev/pandas/pull/36471 added some linting checks (e.g., black, flake8) to a pre-commit workflow which are duplicated in https://github.com/pandas-dev/pandas/blob/master/ci/code_checks.sh. Once we feel good that the pre-commit checks are right we should go ahead and delete them from `code_checks.sh`.

cc @MarcoGorelli 