The idea here is not obvious to a person living in the free world: it is to prevent your "scary, and mighty" standing army shown as weak, and losing in case it got stomped.
Seeing the "tzar's army" being weak will inevitably invite a challenge to his power.
It is disinformation-as-policy to bolster their political might without flexing their full military. The finest example of Hypernormalization.
Embarrassed that their government represents people of my heritage. Путин просто хуйло.
The reason why Wagner exists is quite simple - primarily it vents out all the people who has not found their place in Russia(and prevents their use against those who are in power in Russia) and their main and primary reason to serve in Wagner is being killed in the name of Russia. They are not expected to get back - in Ukraine conflict Wagner people were bombed by Russian army, when they decided to go back. They are expendables from the day they signed up.
That doesn't really matter, though. The thin veneer lets them use their veto in the Security Council, and probably gets China to do so as well.
Same scenario as OJ Simpson publishing the "(if) I did it" book. Everyone knows what's going on. No one can do anything about it.