Lightroom classic is unable to detect people/face for masking.

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Rotating the photo as @Ian Lyons suggested does indeed allow People masking to identify the person:

But there's a gotcha. After applying the People mask and rotating the photo back, the AI Edit Status button will turn yellow indicating the mask needs to be updated. If you click the Update button, the existing computed person mask will get deleted:

So apply all your edits in the order recommended by Adobe and avoid clicking the Update button or giving the menu command Update AI Settings on that photo.