He’s a Putin puppet

A common misconception.

Lukashenko has been around longer the Yeltsin. Putin, Medvedev, and Putin 2: Electric Boogaloo. I would bet money that he'll be around after Putin's demise as well - whenever that will be.

As much of an idiot lackey as he seems - he's always been to squeeze what he wants out of Russia while squeezing from the West as well. Visa relationships, for example - are a good metric for international diplomacy. Americans can travel visa-free through Minsk Airport for up to 30 days. Think about that. And also - he's managed to survive his own coup/revolution attempts. And yes, with Russia's support - but he's still done it.

The war put him in a precarious balancing act where has simultaneously play nice with Moscow without getting Belarusian troops actually involved in battle. It keeps him in power.

I'm not saying Luka is smart or cunning. But he's maintained power for 30+ years. He's experienced in it.

why would Prigozhin cut a deal with him?

Nobody knows.

But I'm speculating Belarus offered him something very special. Maybe Moscow will oust Shoigu, and Belarusian 'diplomacy' will be seen as legitimate.

A distracted Moscow would be a premium opportunity for Belarusian activists and freedom fighters to organize another revolution. Last night, Lukashenko flew his family to Turkey. So... we can speculate as to how confident Luka was feeling.

Was the whole thing a psy-op to give Putin an out?

The "out" would've been for Putin to recall troops to Moscow to 'deal with the Wagner problem'. It would've given him an out and he would've seemed competent to do so.

Afterwards, he can say "its clear need to fix problems in the Russian military before we can help our lost brothers in Ukraine" and call an indefinite ceasefire. Then funnel money into military development indefinitely, like a fascist does.

But that's not what's happening... Wagner might just go back to fighting in Ukraine later today.

The news is happening at lightning speed. Nobody knows what's going on. Absolutely wild times.

What do you mean?

"An agreement was reached on the return of PMC Wagner to their locations. Part of those who will wish to do so, will sign contracts with the Ministry of Defense — this concerns those who did not take part in the march, indeed, there were such formations which, from the very beginning, changed their minds and returned. They even requested to be escorted by the traffic police and other assistance in order to return to their permanent locations,"

more $$$

People say this, but how does any of this benefit Russia?

and mercs are generally a bad idea unless you run them…

Well the entire affair is basically a Prigozin response to Russia wanting to run them closer so they do know that. Interestingly enough his gamble was apparently to check if Russian government is really as weak as western and UA media says and the support in army is crumbling. It turned out that propaganda is wishful thinking and nobody outside Wagner Group supported the endeavour and afaik even a lot of Wagner personnel said they didn't sign up for that.

But, neither side could just admit they were in wrong so that's why Lukashenko proposal came in and now they can just talk and resolve it one way or another.