Qiskit / qiskit-ibm-runtime / 35250870859

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Support dry-run mode when executing a primitive (#3314)

### Summary

Add a `dry-run` flag to existing primitives `run()` methods that, when
passed, causes the job to be an estimation/validation job, as opposed to
a regular job. This is achieved by routing the job to a different
backend based on the original one:
* all public `run()` method gain a `dry_run` flag, defaulting to `False`
* internal methods that do the execution (`QiskitRuntimeService._run()`
and the intermediate ones) gain the flag.
* `QiskitRuntimeService._run()` contains the logic

### Details and comments

Fixes #3312

### AI/LLM disclosure

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

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