Kazakhstan is not listed among the countries

You seem to be reading opposite. The list is the countries which are supported. So if your country is not listed, then you can’t earn. If you look at https://support.brave.com/hc/en-us/articles/6539887971469 I do not see your country, therefore you can’t earn.

That said, Kazakhstan is a country on the list at https://brave.com/transparency/ which means you should be able to opt in and at least view ads, though you won’t be able to connect to a custodial partner or earn BAT for yourself.

Most likely you are seeing what you are because of the country/region settings and/or language settings on your device. For more information on that, check out Rewards are not available in your area