Add generic Fake Backends and update use in Qiskit unit tests

[ElePT]

What should we add?

In order to improve the user-friendliness of fake backends, #9553 presents a multi-step plan to migrate them to the provider. This plan includes the creation of new, non-provider specific fake backends to replace the provider-specific ones in our suite of unit tests, the migration of the provider-specific fake backends to qiskit-ibm-runtime, followed by their deprecation and removal in Qiskit.

Step 1: Introduce alternatives to provider-specific fake backends

The strategy to follow will be different for fake backends of type V1 and V2:

• V2: Their use in tests can be replaced with a fake backend generator/ configurable fake backend. The ground work was laid out in a community PR, and I am taking over the task together with @HuangJunye.
• V1: All uses of V1 backends will be replaced with a few representative fake backends, as the internal structure of BackendV1 does not easily allow for a backend generator.

To make the review process a bit more manageable, the work has now been divided into 3 PRs, where V1 and V2 changes can be reviewed independently:

• 1. Add V2 generic backend: Add fake generic and modify tests #10266. To be backported to 0.46.
• 2. Update rest of V2 tests: Update remaining unit tests to use FakeGeneric #10918 (blocked by Add fake generic and modify tests #10266). To be backported to 0.46.
• 3. Add V1 "generic" backends and update tests: Add generic V1 Fake Backends, replace use in tests #10952. To be backported to 0.46.
• 4. Modify fake backend visual tests and improve documentation (included in removal PR Remove provider-specific fake backends,FakeProvider class and related tools in 1.0 #11376)

Step 2: Migrate IBM-specific fake backends to qiskit-ibm-runtime, deprecate and remove in Qiskit 1.0

• Migration PR: Migrate fake backends from qiskit.providers.fake_provider qiskit-ibm-runtime#1140
• Deprecation PR: Deprecate provider-specific fake backends,FakeProvider class and related tools in 0.46 #11381
• Removal PR: Remove provider-specific fake backends,FakeProvider class and related tools in 1.0 #11376

[mtreinish]

This has been implemented since #11376 merged was the last step on this epic.