BUG/PERF: merge_asof with multiple "by" keys

[lukemanley]

• closes BUG: merge_asof gives incorrect results when by consists of multiple categorical columns with equal, but differently ordered, categories #43541
• 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/v2.2.0.rst file if fixing a bug or adding a new feature.

> asv continuous -f 1.1 upstream/main merge-as-of-multi-by -b join_merge.MergeAsof

.       before           after         ratio
     [59d4e841]       [bfe776d7]
     <main>           <merge-as-of-multi-by>
-      1.66±0.03s         602±50ms     0.36  join_merge.MergeAsof.time_multiby('nearest', None)
-      1.56±0.03s         560±40ms     0.36  join_merge.MergeAsof.time_multiby('nearest', 5)
-      1.48±0.03s         449±50ms     0.30  join_merge.MergeAsof.time_multiby('forward', None)
-      1.60±0.07s         472±30ms     0.29  join_merge.MergeAsof.time_multiby('forward', 5)
-      1.25±0.03s         314±10ms     0.25  join_merge.MergeAsof.time_multiby('backward', None)
-       1.35±0.1s         295±10ms     0.22  join_merge.MergeAsof.time_multiby('backward', 5)

[mroeschke]

I'm assuming this work alright with ExtensionArrays? Do we have tests for merging on by that is a extension column?

[lukemanley]

Yes, this will work with EAs. I've parameterized an existing test to include EA dtypes.

[lukemanley]

Added an additional test as this seems to fix #43541

[WillAyd]

Not super familiar with this code but does hard coding "outer" not have any impact? Wondering if there was a case where two dataframes get joined with very few matches

[lukemanley]

Good point, we can use how=left here. Updated.

[mroeschke]

Thanks @lukemanley