Process Fucntion refactor to Enforce return_jacp_stacked=True

[RohitP2005]

Description

Refactored the process function in base_solver.pyto simplify its logic and improve maintainability.

Fixes #4970

Type of change

Refactor (non-breaking change that improves code structure) to the process function in the base solver to enforce return_jacp_stacked=True .

Important checks:

Please confirm the following before marking the PR as ready for review:

• No style issues: nox -s pre-commit
• All tests pass: nox -s tests
• The documentation builds: nox -s doctests
• Code is commented for hard-to-understand areas
• Tests added that prove fix is effective or that feature works

[RohitP2005]

@martinjrobins I've refactored the process function in base_solver.py to simplify the logic Could you please take a look at the changes? If everything looks good, we can go ahead and check the CI tests.

Thanks!

[RohitP2005]

Hi @RohitP2005, I think there is much more to do on this (than just removing the arg. Have you run the tests locally?

Yes , I ran the tests locally and there are errors that needs to addressed. we fix those issues and make the requested changes.