Support PETSc >= 3.22

[A-CGray]

Purpose

Expected time until merged

Type of change

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (non-backwards-compatible fix or feature)
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Documentation update
• Maintenance update
• Other (please describe)

Testing

Checklist

• I have run ruff check and ruff format to make sure the Python code adheres to PEP-8 and is consistently formatted
• I have formatted the Fortran code with fprettify or C/C++ code with clang-format as applicable
• I have run unit and regression tests which pass locally with my changes
• I have added new tests that prove my fix is effective or that my feature works
• I have added necessary documentation

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 73.24%. Comparing base (a86e9d9) to head (7cebe69).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #107      +/-   ##
==========================================
- Coverage   73.31%   73.24%   -0.08%     
==========================================
  Files           6        6              
  Lines         757      755       -2     
==========================================
- Hits          555      553       -2     
  Misses        202      202              

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