I haven't seen news on this one way or the other - unfortunately I think it'll be a case of waiting until the new year and seeing what happens. As a comparison, when the visa waiver scheme was first launched, it was always "provisional until 31st December 20xx" (the following year) and we always had to wait until a few days into the new year to confirm it had indeed been extended.
I was feeling quite confident KZ would reinstate the visa-waiver from 1st Jan 2022 until the Omicron wave started, now I'm not so sure. Since 3rd December new travel restrictions have applied:
https://www.inform.kz/en/kazakhstan-to- ... n_a3868663Arrivals from the countries affected by the new Omicron strain, namely, Israel, Czech Republic, the Netherlands, Belgium, the UK, Italy, Germany, Australia and Canada, must present negative PCR test despite vaccination against coronavirus and self-isolate for seven days.
If you're lucky enough to be from Germany / Netherlands / Poland / Hungary / UK then you should be able to get a tourist visa through the "direct flight" provision. Otherwise I think it'll be a matter of waiting to see if any relaxations are announced in January.
For what its worth, there seems to be a lull in Covid cases within Kazakhstan recently. The excess deaths shown by the guys at World Mortality Dataset seems to be a realistic measure for the countries it covers. It shows Covid deaths in Kazakhstan coming down in September / October from a peak in August: