Hi, it does not really work that way. First of all, those border crossing are not open to tourists, as in, people who are not living the bordering countries them selves. Check out the GREEN markers on this map: https://caravanistan.com/border-crossings/
Secondly, you would already need special border zone permits all over to even reach this parts and get through military checkpoints.
And third, I would think parts of these roads will be so bad that it would be very time consuming or you may need quite a good car.
If you don't have any specific interest in this corner/tip of Kazakhstan, then I would suggest to go to follow the main routes, so via Semey somewhere enter Russia, drive to Barnaul, and go over the main road to Tasjanta / Tsaganuur crossing. (but don't go into Tsaganuur town itself, people try to get money out of tourists or steal things. The rest of Mongolia is okay, Olgii is already much better)
This described road is mostly asphalt, and is actually a nice drive through Altai. You will even see some signs pointing to place of interest in the Russian part of the Altai.