I've checked this option in settings that says: "Registration requires administrator's approval:" in kentico10. and in my custom registration web part I've unchecked Enable user after registration. but I can't see unable users waiting for the approval tab. https://i.stack.imgur.com/QjxfE.png like below picture.
I believe the user has to be enabled to show in Waiting for Approval list. So updating your web part to enable the user should resolve it. Been a while since I've had to work with that so I could be wrong.
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