I don't understand the logic here. When the putsch occured and then ignomously fizzled out, I saw Putin as weak for letting Pringles walk out with a (relative) slap on the wrist. Taking Prigo out of the picture was overdue. Obviously, anyone would feel threatened by an semi-autonomous mercenary army, so removing its leadership and breaking it up is just a rational course of action that probably should have been done sooner from that POV

then this will just further enforce option that russia can not be trusted to do anything it says and that putin is weak and threatened

If they let him live, they're weak. If they kill him, they're weak.

During the cold war, the anticommunist ideological framework could transform any data about existing communist societies into hostile evidence. If the Soviets refused to negotiate a point, they were intransigent and belligerent; if they appeared willing to make concessions, this was but a skillful ploy to put us off our guard. By opposing arms limitations, they would have demonstrated their aggressive intent; but when in fact they supported most armament treaties, it was because they were mendacious and manipulative. If the churches in the USSR were empty, this demonstrated that religion was suppressed; but if the churches were full, this meant the people were rejecting the regime's atheistic ideology. If the workers went on strike (as happened on infrequent occasions), this was evidence of their alienation from the collectivist system; if they didn't go on strike, this was because they were intimidated and lacked freedom. A scarcity of consumer goods demonstrated the failure of the economic system; an improvement in consumer supplies meant only that the leaders were attempting to placate a restive population and so maintain a firmer hold over them. If communists in the United States played an important role struggling for the rights of workers, the poor, African-Americans, women, and others, this was only their guileful way of gathering support among disfranchised groups and gaining power for themselves. How one gained power by fighting for the rights of powerless groups was never explained. What we are dealing with is a nonfalsifiable orthodoxy, so assiduously marketed by the ruling interests that it affected people across the entire political spectrum.

If this is backed up at all by anything like a russian source

The Guardian is reporting this:

The cause of the crash was not immediately clear, but Prigozhin’s longstanding feud with the military and the armed uprising he led in June would give ample motive to the Russian state for revenge. Media channels linked to Wagner quickly suggested that a Russian air defence missile had shot down the plane.

https://www.theguardian.com/world/live/2023/aug/23/russia-ukraine-war-live-updates-drones-downed-moscow#top-of-blog

The capitol riot was a threat to our precious democracy! / prigozhin’s coup attempt shows how weak putler is!

Russia decapitation their own PMC org that tried to coup them does not mean they cannot be negotiated with