Deletes the integration, then removes the paging extension it created and refreshes call routing. If that extension is still used by one or more call flows the call answers 409 and nothing is deleted; if the reference check cannot be completed it answers 502 and, again, nothing is deleted. The follow-up cleanup is best-effort and only logged if it fails, so a 200 does not guarantee the paging extension is gone, and an unknown ID surfaces as a 500 rather than a 404. The success body is {}.