Follow up work for custom program removal

[jyu00]

What is the expected feature or enhancement?

Some follow up work for custom program removal:

• Make service.run() and session.run() private (after deprecation period). These methods should no longer be called directly, as everything should be sampler/estimator/backend.run.
• Replace any mention of programs with primitives in public APIs (e.g. qiskit_ibm_runtime.__init__.py)
• Cleanup unused exceptions (e.g. RuntimeDuplicateProgramError)
• Change job.program_id to job.primitive_id (after deprecation period)

Acceptance criteria

The list above.