docs(python): Improve DataFrame.write_database docstring

[rodrigogiraoserrao]

Fixes #19181

cc @alexander-beedie

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 79.95%. Comparing base (44cf3ad) to head (638579a).
Report is 3 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #19189   +/-   ##
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  Coverage   79.94%   79.95%           
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  Files        1526     1526           
  Lines      208499   208499           
  Branches     2416     2416           
=======================================
+ Hits       166692   166700    +8     
+ Misses      41259    41251    -8     
  Partials      548      548           

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[alexander-beedie]

I'd omit line 3895 ("see the documentation") - the reader is already in the documentation (not the documentation of the adbc/alchemy projects, but this suggestion doesn't link to those). But good improvement otherwise :)

[rodrigogiraoserrao]

I actually think that that sentence is important because it makes it obvious to the user that there is an extra level of indirection (see the docs for “the appropriate method”) that they need to follow for the full info.
Either way, I deleted that sentence in 638579a.