Remove qiskit-ibm-provider support

[1ucian0]

Summary

qiskit-ibm-provider does not have support since Jul 2024. Time to clean its handling?

Details and comments

I tried to find all the places and branches that handle qiskit-ibm-provider cases. Not sure if I found all of them.

PR checklist (delete when all criteria are met)

• I have read the contributing guide CONTRIBUTING.md.
• I have added a release note file using reno if this change needs to be documented in the release notes.

[wshanks]

Thanks for looking into this @1ucian0. As far as I can tell, the retrieve_job usage is safe to remove. With the other usage, I think we need to update the code a bit more. If we take qiskit-ibm-runtime as the primary target interface (trying to avoid calling it a "provider" to avoid confusion), then what the code calls a "provider" should now be QiskitRuntimeService instead of IBMProvider. So think we could keep some of the things you remove here if we change to look for service instead of provider. Confusingly, the code refers to the class for gettings jobs/backends as the provider and the experiments service as service but now qiskit-ibm-runtime calls the provider-like thing service as well, so there are two services to track.

[wshanks]

Thanks, @1ucian0! I incorporated changes to the parts of the code you highlighted here into #1502.