What a terrible design- designed to fail.
It seems unlikely that you would be able to get another suitable motor with the exact screw drive, without buying the same part again.
My first though is that a simple sleeve held in place by radial screws and adhesive would couple the two shafts back together, but that depends on there being enough room for the sleeve on the main housing.
Someone with a lathe, ideally a hobbyist model maker, would be able to design and make you a custom sleeve quite easily and cheaply.
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