Its not that hard.
In 2016, the army rebelled in Turkey and dropped bombs on the capital. Erdogan still made it out stronger than ever.
Same will happen in Russia. If the Wagner group gets enough support from the military, theyll oust Putin. This is very unlikely but theres a slight chance it can happen, but only if there are high ranking Russian army generals that support Wagner group.
But if Putin makes it out of this without losing his presidency, he will find a way to still get popular support.
Cause its all about popular support end of the day.