Add new error handling capability

[SeanBryan51]

This change adds a new error handling capability. This is basically a more polished version of the error handler that was introduced with the parallel I/O changes (#641) and addresses broader error handling requirements.

Closes #699

Type of change

Please delete options that are not relevant.

• New feature
• New or updated documentation

Checklist

• The new content is accessible and located in the appropriate section
• I have checked that links are valid and point to the intended content
• I have checked my code/text and corrected any misspellings

Testing

• Are the changes bitwise-compatible with the main branch? If working on an optional feature, are the results bitwise-compatible when this feature is off? If yes, copy benchcab output showing successful completion of the bitwise compatibility tests or equivalent results below this line.

2026-03-04 12:51:46,713 - INFO - benchcab.benchcab.py:380 - Running comparison tasks...
2026-03-04 12:51:46,738 - INFO - benchcab.benchcab.py:381 - tasks: 168 (models: 2, sites: 42, science configurations: 4)
2026-03-04 12:54:35,161 - INFO - benchcab.benchcab.py:391 - 0 failed, 168 passed

Please add a reviewer when ready for review.

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📚 Documentation preview 📚: https://cable--700.org.readthedocs.build/en/700/