As for the continuation of the story, Putin and Prigozhin understood differently the deal they made via Lukashenko. Putin won't fire Shoigu, which was the main condition of Prigozhin. Not because Putin doesn't want to, he can't.
The fact that yesterday, Alexei Diumin was called to the Kremlin means that Putin counted on Prigozhin to eliminate Shoigu to replace him with his long-time bodyguard and loyalist Diumin finally.
In 2021 after the Duma elections, Putin already tried to replace Shoigu with his other former bodyguard Yevgeny Zinichev, who then occupied the same position as earlier Shoigu - the head of the Emergency Ministry.