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The standard syzygy bases of course do, they are designed for practical play. Some table base developers in the past took pleasure announcing mate in several hundred moves in certain positions and this had made headlines in the past, hence the confusion maybe.

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Ah, cool, interesting.

Does the 50 turn rule make the analysis harder or easier? My gut says easier because it creates some limit that should, I guess, let you prune some extra cases somehow… but it does add some extra state which is weird. Two otherwise identical board states become no longer identical depending on how you got there…

You don't keep track of it as extra state - positions are already processed in increasing order of shortest mate, you stop once you hit 50.

That's not really how it works, though, as the counter is reset back to 0 once a capture happens or a pawn is moved (as both of those are irreversible and thus represent some abstract proof of progress towards a resolution of the game).

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