fix(python): Ensure we don't close extant adbc connections in write_database

[alexander-beedie]

Closes #17293.

Extant ADBC connections were implicitly closed in write_database via context manager; fixed, and added coverage.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 80.73%. Comparing base (d444b79) to head (f8b5968).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #17298      +/-   ##
==========================================
+ Coverage   80.72%   80.73%   +0.01%     
==========================================
  Files        1475     1475              
  Lines      193162   193162              
  Branches     2751     2751              
==========================================
+ Hits       155922   155948      +26     
+ Misses      36732    36706      -26     
  Partials      508      508              

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