Migrate automatic transcription checks to the new check system

[TimJentzsch]

Relevant issue: Closes #330

Description:

This PR migrates the automatic transcription checks to the new button-based system (used by the check Slack command).

It also includes some minor changes to the button workflow, removing the "Warn" button in the comment pending state and using the default style for the "Warn" button.

Checklist:

• [x] Code Quality
• [x] Pep-8
• [ ] Tests (if applicable)
• [x] Success Criteria Met
• [x] Inline Documentation
• [ ] Wiki Documentation (if applicable)