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Remove use of deprecated objects in `BasicSimulator` (#13743)

* Refactor BasicSimulator not to rely on assemble or qobj. Drop support for c_if (deprecated) and providing parameter bounds to the "run" method.

* Code cleanup and style fixing

* Add reno

* Address small oversights

* Apply suggestions from Eli's code review

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Fix handling of backend options in both BasicSimulator and BackendV2. Add unit tests. Rename kwargs to unify use of options with aer simulator and update documentation to reflect actual usage.

* Document header in docstring

* Fix lint

* Apply suggestions from Eli's code review

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

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Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

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