Remove exception and error message statefullness from run models

[oyvindeide]

Issue
Resolves #my_issue

Approach
Short description of the approach

(Screenshot of new behavior in GUI if applicable)

• PR title captures the intent of the changes, and is fitting for release notes.
• Added appropriate release note label
• Commit history is consistent and clean, in line with the contribution guidelines.
• Make sure tests pass locally (after every commit!)

When applicable

• When there are user facing changes: Updated documentation
• New behavior or changes to existing untested code: Ensured that unit tests are added (See Ground Rules).
• Large PR: Prepare changes in small commits for more convenient review
• Bug fix: Add regression test for the bug
• Bug fix: Create Backport PR to latest release

[sondreso]

Nice improvement!

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 94.44444% with 1 line in your changes missing coverage. Please review.

Project coverage is 90.87%. Comparing base (50a9869) to head (463a773).
Report is 2 commits behind head on main.

Files	Patch %	Lines
src/ert/run_models/base_run_model.py	93.75%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #8375      +/-   ##
==========================================
- Coverage   90.88%   90.87%   -0.01%     
==========================================
  Files         347      347              
  Lines       21076    21064      -12     
==========================================
- Hits        19154    19142      -12     
  Misses       1922     1922              

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