Make local jobs more like remote jobs

[jyu00]

What is the expected feature or enhancement?

The local testing mode is design to be as closely as possible to remote execution. #1605 made local (fake) backends more similar to IBMBackend. We should also make jobs returned in local mode more similar to RuntimeJobV2. One example of such discrepancy is #1939.

Acceptance criteria

Job returned in local testing mode should have the same methods as RuntimeJobV2, including (but not limited to) backend(), metrics(), usage(), etc

[yaelbh]

Do you think the old issues Qiskit/qiskit-aer#1567 and Qiskit/qiskit#8523 are relevant here?