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Hi, I doubt very much, that you will be able to find that little "worm shaft" anywhere on its own - to start with, I think it is part of the rotor of that motor.
So, if you are lucky, you might get the motor somewhere.
I googled and found a few links for you - may it is what you are looking for: https://www.ebay.com/itm/234371174078
(plus check the P/N given at the item specifics on ebay - that might bring you further in finding those parts elsewhere.
Your part looks different somehow...
And if you are very lucky, maybe you can use this generic part from Aliexpress? :
I am not saying that this is the exact part you are looking for, but if they have something like this, it might be worth looking there for the exact part you are looking for - and if that link does not work, look in Aliexpress for: