Qiskit / qiskit-ibm-runtime / 35360540083

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Ensure Primitives backend method disallow none (#3343)

### Summary

Follow up to comments in #3333, revising type hints and
`get_mode_service_backend`. All paths do return a `backend` object and a
`service` object, with the `mode` item of the tuple being able to return
`None`.

Adjusted the `.backend()` returns annotation accordingly, and revised
some type hints in general.

### Details and comments

The original comments also suggested taking the chance and avoid some
`if` logic that takes into account `service`, `mode`, and `backend` for
routing to the right `_run()` method. Simplification _can_ be done in
`base_primitive.py` and `noise_learner.py`, but since we are on the
verge of considering them deprecated, I opted not to include the
changes.

Fixes N/A

### AI/LLM disclosure

- [x] I didn't use LLM tooling, or only used it privately.

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