Rework solve slightly

[je-cook]

Description

Some more code split out from #4308 this time around some small solver related things and removing some unnecessary files (final and output)

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 12.83422% with 163 lines in your changes missing coverage. Please review.
✅ Project coverage is 49.24%. Comparing base (b9b6a45) to head (b6fd9ec).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
process/core/solver/solver_handler.py	9.45%	67 Missing ⚠️
process/main.py	13.04%	40 Missing ⚠️
process/core/caller.py	13.79%	25 Missing ⚠️
process/core/solver/constraints.py	12.00%	22 Missing ⚠️
process/core/solver/solver.py	33.33%	4 Missing ⚠️
process/models/tfcoil/superconducting.py	33.33%	4 Missing ⚠️
process/core/scan.py	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4508      +/-   ##
==========================================
+ Coverage   49.14%   49.24%   +0.10%     
==========================================
  Files         152      150       -2     
  Lines       29803    29746      -57     
==========================================
+ Hits        14647    14649       +2     
+ Misses      15156    15097      -59     

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