fix: stabilize grouped correlation with centered moments

[bvolpato]

Which issue does this PR close?

No linked issue. The regression below reproduces the problem on current upstream.

Rationale for this change

Grouped CORR uses raw sums whose subtraction loses precision when values have a large common offset. It can return a negative correlation for a column correlated with itself:

SELECT g, corr(x, x)
FROM (VALUES
  (1, 1000000000.0),
  (1, 1000000007.0),
  (1, 1000000015.0),
  (2, 1.0)
) AS t(g, x)
GROUP BY g;

Group 1 can return -1 instead of 1.

What changes are included in this PR?

• Use paired Welford updates and centered moments for grouped correlation.
• Merge partial states using weighted mean differences, applying weights before multiplying deltas to avoid avoidable intermediate overflow.
• Match the scalar CORR state layout across update, merge, singleton conversion, and preserving/draining emission.
• Add regressions for large offsets, multiple batch sizes, scalar/grouped state interchange, and large-range merges, plus a grouped self-correlation case in aggregate.slt.

What is the testing strategy for this PR?

• The large-offset and scalar/grouped state compatibility tests fail against upstream production code at 35f58f53cde2f634c21f6370e385cf1d7e9bc55c and pass with the fix.
• cargo test --locked -p datafusion-functions-aggregate --lib: 210 passed.
• cargo fmt --all -- --check and git diff --check passed.
• Draft pending all-target/all-feature Clippy, the extended workspace suite, and execution of aggregate.slt.
• The H2O groupby q09 benchmark exercises CORR. Comparison against main is still pending.

Are there any user-facing changes?

Grouped CORR produces stable results for the covered large-offset inputs. Floating-point results can differ in their final bits. SQL signatures and output types remain unchanged.

Downsides

Centered updates add arithmetic, including per-row divisions. The grouped intermediate state representation changes from raw sums to centered moments, so partial states produced by the old implementation cannot be mixed with the new representation.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 91.16466% with 22 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.61%. Comparing base (35f58f5) to head (7bdd886).

Files with missing lines	Patch %	Lines
datafusion/functions-aggregate/src/correlation.rs	91.16%	3 Missing and 19 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #24953      +/-   ##
==========================================
- Coverage   81.61%   81.61%   -0.01%     
==========================================
  Files        1124     1124              
  Lines      411978   412086     +108     
  Branches   411978   412086     +108     
==========================================
+ Hits       336236   336318      +82     
- Misses      55936    55941       +5     
- Partials    19806    19827      +21     

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