It is much easier to get while you’re in KZ. I wish I got it there instead of dealing with this here in the US. Plus you’re facing a risk of not being let out of the country when you exit on your K1, I got lucky but I don’t recommend it.
This permission paper is something that the government of KZ requires for those moving to live permanently abroad. During exit checks at the airport, they can stop you from leaving the country without it and there’s nothing you can do. You’ll have to stay back and get the paper before attempting to leave again.
I got it here at the KZ consulate but it took forever because the migration police sends it to the US via regular mail (Kaz pochta). The consulate told me it’s lost and “I should be okay to exit without it, they probably see it in the system “. Well that answer didn’t satisfy me so I pushed. They ordered another one and luckily it came but the back and forth was annoying.
It’s interesting they mentioned it at your interview; they haven’t at mine and I wonder if it’s because there’s been incidents of it being requested when exiting the country. I know some people who have been barred from exiting, they were DV applicants.
Prepare to hand in your national ID whether you do it abroad or in the country. You won’t be able to have a National ID any longer and if you request it in the future be advised that you will lose the permission to live abroad and you’ll have to apply for it all over again.