Reimplemented Pearson's correlation to use two pass Welford's model

[eicchen]

• closes BUG: Pearson correlation outside expected range -1 to 1 #59652
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

This improves numerical stability for values that are really large or small such as the example given in the original issue.

[Alvaro-Kothe]

Can you run the benchmarks?

[eicchen]

I've already run the relevant benchmarks. Unsurprisingly, we are looking at performance decrease in stat_ops.Correlation. I've looked into other ways of solving the issue while keeping the online Welford.

The problem stems from the co-moment calculations at large/small values and the asymmetric nature of Welford's Algorithm. The three values above are mathematically the same, however, when calculating the values provided in the test case, there are always two that are correct and one that is not.

We could pick the value of the pair that match as a redundancy measure. Theoretically, it can only reduce our errors compared to our current version, as the values should be equal. But without a larger test pool, I wouldn't be confident enough to put it in a release version. Two-pass provides the best numerical stability at the cost of performance.