This change improves several aspects about the way `ExperimentData`
works with "providers." Here "provider" is generalized beyond
`qiskit.providers.Provider` to any object which can provide a `Job`-like
object with data about an experiment's circuit execution. This
generalization is needed because `qiskit-ibm-runtime`, the main provider
that Experiments integrates with, does not use the `Provider` class, so

* Replace references to `qiskit.providers.Provider` and
`qiskit.providers.Job` with custom interface definitions using
`typing.Protocol`. The new interfaces document the API Experiments needs
for working with these objects.
* Improve type hints and type checking related to providers, jobs, and
results, using the new protocol classes.
* Infer `IBMExperimentService` authentication parameters from a
`qiskit_ibm_runtime.QiskitRuntimeService` instance in the same way that
the inference used to work with `qiskit_ibm_provider.IBMProvider`.
* Delay inferring an `IBMExperimentService` from a backend or provider
until `ExperimentData` tries to communicate with the experiment service.
With the fix to infer the authentication parameters from
`QiskitRuntimeService`, this delay is needed to avoid breaking existing
code that creates an `ExperimentData` instance and then tries to set a
custom experiment service for it, relying on the fact that inferrence
did not work for `QiskitRuntimeService`, since setting the service on
`ExperimentData` after it has already been set once raises an exception.
* Remove dead code, both helper functions that are not called anywhere
in the repository and code paths only relevant to qiskit-ibm-provider,
like references to `time_per_step()`. Since `qiskit-ibm-provider` has
long been deprecated and unsupported by IBM Quantum, removing support
for it is not treated as a breaking change.
* Handle some optional data types better (like result objects that might
have a `metadata` attribute).

(cherry picked from commit 2d48547)

This change improves several aspects about the way `ExperimentData`
works with "providers." Here "provider" is generalized beyond
`qiskit.providers.Provider` to any object which can provide a `Job`-like
object with data about an experiment's circuit execution. This
generalization is needed because `qiskit-ibm-runtime`, the main provider
that Experiments integrates with, does not use the `Provider` class, so

* Replace references to `qiskit.providers.Provider` and
`qiskit.providers.Job` with custom interface definitions using
`typing.Protocol`. The new interfaces document the API Experiments needs
for working with these objects.
* Improve type hints and type checking related to providers, jobs, and
results, using the new protocol classes.
* Infer `IBMExperimentService` authentication parameters from a
`qiskit_ibm_runtime.QiskitRuntimeService` instance in the same way that
the inference used to work with `qiskit_ibm_provider.IBMProvider`.
* Delay inferring an `IBMExperimentService` from a backend or provider
until `ExperimentData` tries to communicate with the experiment service.
With the fix to infer the authentication parameters from
`QiskitRuntimeService`, this delay is needed to avoid breaking existing
code that creates an `ExperimentData` instance and then tries to set a
custom experiment service for it, relying on the fact that inferrence
did not work for `QiskitRuntimeService`, since setting the service on
`ExperimentData` after it has already been set once raises an exception.
* Remove dead code, both helper functions that are not called anywhere
in the repository and code paths only relevant to qiskit-ibm-provider,
like references to `time_per_step()`. Since `qiskit-ibm-provider` has
long been deprecated and unsupported by IBM Quantum, removing support
for it is not treated as a breaking change.
* Handle some optional data types better (like result objects that might
have a `metadata` attribute).<hr>This is an automatic backport of pull
request #1502 done by [Mergify](https://mergify.com).

Co-authored-by: Will Shanks <[email protected]>