Add state permissions and allow state changes
As far as I'm aware, there's no way to give permission to manage a specific state, nor workflow for that matter.

The only permission to cover these is administer workflows and it covers all workflows.

You can see this by looking the content_moderation.routing.yml

content_moderation.workflow_type_edit_form:
path: '/admin/config/workflow/workflows/manage/{workflow}/type/{entity_type_id}'
defaults:
  _form: '\Drupal\content_moderation\Form\ContentModerationConfigureEntityTypesForm'
  _title_callback: '\Drupal\content_moderation\Form\ContentModerationConfigureEntityTypesForm::getTitle'
requirements:
  _permission: 'administer workflows'


EDIT
That is with the default permissions.