Most likely. Unless the army uses this as a chance to mutiny. But seeing as the army is actually involved in some pretty intense combat right now, and Wagner was just sitting behind the lines it may be that the views on Wagner are very mixed. The troops have also been fighting hard. Wagner which was just deployed at Bakhmut then got to take a break after that but keep complaining.
But to say that Prigozhin was necessarily a threat to Putin is kind of a stretch. Putin could have easily fled Moscow. If Prigozhin occupied Moscow what then? He isn't going to rule Russia with just 30,000 men. Moscow is not all of Russia. If he damages the war effort then he loses support. The populace wouldn't have supported him. The Russian army could be deployed to attack him in Moscow. This had civil war potential, it was reminiscent of 1991. So what the hell was he thinking?
On the immediate front line? Nothing except for maybe morale. Maybe Wagner has control of key installations though, like Rostov.
It could affect army logistics. Prigozhin could try something again though, which could hurt the front line.
Wagner has been relaxing since Bakhmut ended. Current operations have little or nothing to do with Wagner at the moment. So it was not a major blow to the army or current operations.
Yeah who knows. Wagner might do something again. The army might mutiny. This is a hit to Putin's prestige for sure. My best guess is that Prigozhin will go missing, maybe taken in a van. Or will literally be found dead somewhere. Maybe he will run away and seek asylum.
Let me put it like this. Prigozhin has two prior convictions in Russia. I am hardly surprised that a guy like Prigozhin, who leads an entire Corps of criminals, and whose officers are ex-military most of whom have criminal records, would then carry out sedition over something so petty. It isn't too surprising at all considering how much he has been mouthing off the past months and how vocal and irreverent he was being. The man clearly has low impulse control as his two convictions demonstrate.
If not this uprising then he was bound to be a liability given that he leads a heavily armed private army. If I was Putin then Prigo would have been six feet under the moment he started mouthing off. Even if he doesn't do anything again, he is still a huge liability because he acts like a mobster with low impulse control. He reminds me of Joe Peschi from Goodfellas (or Casino).