Prigozhin’s actions can only be understood based on business logic. According to official data, the equivalent of more than a billion euros was spent annually from the Russian budget on the maintenance of the Wagner PMC. Prigozhin will try by all means to obtain similar funding again from any source.
Lukashenko has no such money, so he will not be able to hire Prigozhin’s army. African and Asian clients are unlikely to compensate for the loss. Moreover, after the rebellion against the customer, Prigozhin’s image on the global market of PMC services will be formed as an unpredictable and dangerous partner, which is hardly worth doing business with.
So the lost revenues Prigozhin can find only in the same Russian budget. The bloody cook has either to disband the army, which he is obviously not going to do, or force the Kremlin to pay for the war again. However, there is no war in Belarus. This means that Prigozhin will have to bring it there.
His options for action may be as follows.
1. Going to Kyiv.
For an attempt to open a northern front against Ukraine, the Kremlin is able to pay well. However, this is a very dangerous project for Prigozhin. Russian troops will not be able to help him seriously now, and Belarusian troops will not help him. In such a situation, he may be defeated and lose a large part of his already depleted army. Therefore, it is unlikely that he will go for it.
Lukashenko, too, would probably be against it. After all, when repulsing such an attack, the Ukrainians, together with the Belarusian volunteers, may enter Belarus and start a liberation campaign to overthrow the dictatorship.
2. A new military blackmail of the Kremlin, a march on Moscow in order to make the authorities pay.
It is unlikely that Prigozhin would take such a risk. He must realize that he is unlikely to come out of such a mess alive a second time. Putin will try to finish off his rabid cook for sure.
3. Seizing power in Minsk and trying to sell Belarus to the Kremlin.
This option seems to me the most likely. The Belarusian army is weak, it will not be able to resist Prigozhin’s select fighters. An attack on Minsk would be much easier than on Moscow or Kyiv.
Prigozhin is in a position, Bob Denard style, to seize power in Belarus and put some puppet of his there. He can also ask Putin to accept “liberated Belarus” into Russia.
In this case, the bloody cook will become a mega-hero in Russia (Putin failed in Ukraine, and he took Belarus) and will be able to put any conditions to the authorities. And in Belarus, a war will inevitably ensue (the Belarusians will take up arms), in which the main pro-Russian force will be the same Wagner PMC. This means that Prigozhin’s business (trade in death) will again go well.