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Forged, cast and machined parts of equal dimensions have entirely different grain structures.

They have different grain flow. The strength is almost entirely depending on the metallurgy.

My understanding was that forging is work hardening (but hard and strong are not the same thing), annealing cancels it out, which is why quenching and tempering are important.

Also the story of the structure of the metal is a bit different when you've folded it 100's of times. No blacksmith or foundry is getting that sort of fine work in their material.

Forging squeezes the slag out, thereby purifying the steel. As far as I am aware this was the primary mechanism by which folding steel (which was done about a dozen times, not hundreds; those larger numbers come from 2^[n folds]) strengthened Japanese blades.

Was. These days the labor involved in hand-forging a part dominates and cast alloys are everything anyone uses for anything, outside of oddball boutique communities like fancy knife aficionados.