If what Prigozhin and Wagner are doing is NOT a coup or attempt at civil war,...here is one potential historical explanation.
If Prigozhin's withdrawal is in fact an attempt at attaining concession to get a higher level of command of the Russian army, if Prigozhin succeeds in seizing power, then Ukraine could be in great trouble.
In the middle of the Thirty Years' War (1618-1648), the Holy Roman Emperor Ferdinand II reappointed a Czech leader of the mercenary corps - Wallenstein. This man was the most capable military genius of his time. He led the Holy Roman Empire's mercenary corps northward, defeating first Saxony and then Denmark, and extending the Holy Roman Empire's physical control to the Baltic Sea. However, he was forced to withdraw from the kingdom due to the exclusion of other great nobles.
However, when the empire's clutches reached the Baltic Sea in the north, it caused anxiety among the Northern European nations. The second military genius of the time, King Gustav II of Sweden, led his army southward and became the savior of the Protestant Union. Gustav II was known for his amazing ability to innovate. He was the inventor of the line-of-sight tactic, which was subsequently used in Europe for over 200 years.
When this military genius appeared on the battlefields of the Thirty Years' War, the tide of battle was immediately turned, and at the Battle of Breitenfeld in 1631, the Swedish army's line tactics completely crushed the forces of the Holy Roman Empire. Soon after, Count Tilly, the empire's commander, was killed in battle and the empire was in desperate straits.
At this crisis point, the Holy Roman Emperor Ferdinand II had to ask Wallenstein to rejoin him. However, Wallenstein refused at this time. It turned out that Wallenstein did not want to be excluded by the nobles again, so he asked for the supreme and sole command of the empire. The emperor did not agree at first, but Wallenstein did not want to come back, so the emperor had no choice but to agree to Wallenstein's condition and let him have the supreme and sole command of the empire.
With the command, Wallenstein was no longer under the control of other nobles. He took a bold step forward and used his talents to the fullest. At the Battle of Lutzen in 1634, Wallenstein's army killed King Gustav II of Sweden on the spot, eliminating a major threat for the empire.
It was Wallenstein's concession that allowed him to gain more power and to kill Gustav II. Four hundred years later, when the Ukrainian counterattack was imminent and Russia needed troops the most, Prigozhin, who was doing less poorly in Bakhmut than most all other Russian commanders, suddenly announced his withdrawal with the Wagner group and clearly expressed his dissatisfaction with his superiors. Perhapst Prigozhin's real goal was also to seize a higher military command.
While everyone is cheering for more internal discord in Russia,...what if Prigozhin really is that cagey and smart like a fox? Putin certainly is angry with Shoigu and just about everyone else who lied to him before the war and have failed him since. Whether or not Pregozhin possesses any military "genius" (which in my opinion would be a stretch to claim), he certainly has been far more effective with Wagner than just about anyone else on the Russian side in this theater.
It is significant that Prigozhin has criticized everyone EXCEPT Putin. Thus, is it conceivable Prigozhin could be trying to pull a Wallenstein? Consider the cover this gives Putin. If Putin has to put down a rebellion by Wagner and Prigozhin, it provides the excuse for whatever gains Ukraine makes this summer during their offensive, claiming Russia would have fully thwarted the Ukrainians and their NATO running dogs had it not been for having to withdraw assets from inside Ukraine to deal with it. Likewise, declaring a rebellion or civil war is underway would also give political cover for the unpopular task of declaring another general mobilization and induction of more conscripts. OR,...if Putin should give Prigozhin a Wallenstein-like upgrade, he can make much the same excuse for all the failures up until now, declaring that Shoigu and others were criminal in their duties and at fault for all that has happened. Whichever one Putin chooses may well depend upon public perception of Prigozhin.