Rename solver vars to style guide

[chris-ashe]

Description

Closes #4274

🔄 Renames

• ioptimz -> i_process_run_mode
• minmax -> i_figure_merit
• neqns -> n_equality_constraints
• nineqns -> n_inequality_constraints (shouldn't really be used in input files)

Checklist

I confirm that I have completed the following checks:

• My changes follow the PROCESS style guide
• I have justified any large differences in the regression tests caused by this pull request in the comments.
• I have added new tests where appropriate for the changes I have made.
• If I have had to change any existing unit or integration tests, I have justified this change in the pull request comments.
• If I have made documentation changes, I have checked they render correctly.
• I have added documentation for my change, if appropriate.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 54.12844% with 50 lines in your changes missing coverage. Please review.
✅ Project coverage is 49.32%. Comparing base (d353420) to head (169beb7).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
process/core/io/plot/summary.py	0.00%	9 Missing ⚠️
process/core/caller.py	0.00%	8 Missing ⚠️
process/core/solver/solver_handler.py	0.00%	6 Missing ⚠️
process/core/io/in_dat/base.py	28.57%	5 Missing ⚠️
process/core/init.py	88.88%	3 Missing ⚠️
process/core/solver/constraints.py	0.00%	3 Missing ⚠️
process/core/solver/objectives.py	25.00%	3 Missing ⚠️
process/core/io/vary_run/tools.py	33.33%	2 Missing ⚠️
process/core/solver/evaluators.py	0.00%	2 Missing ⚠️
process/core/solver/solver.py	0.00%	2 Missing ⚠️
... and 5 more

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #4481   +/-   ##
=======================================
  Coverage   49.31%   49.32%           
=======================================
  Files         150      150           
  Lines       29769    29802   +33     
=======================================
+ Hits        14682    14700   +18     
- Misses      15087    15102   +15     

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