Hey,
Bi-directional contract testing is a consumer pact file compared against a static contract (OAS file is currently the only supported)
Consumer driven contract testing with Pact, is performed against a locally running provider
https://docs.pact.io/provider
This wouldn't be your live provider, as you would get the feedback as to breaking changes post deployment which is too late.
There is a case where you may want monitoring on your endpoints post deployment, to ensure they work but that is beyond the scope of a contract test, (more a health check / smoke test / canary test ), although I think there is a use case, where a consumer contract file could be used as the input for a live verification. I would consider this FAQ question around 3rd party systems
https://docs.pact.io/faq#why-pact-may-not-be-the-best-tool-for-public-testing-apis as the caveats are the same for testing against a live provider