Honestly, the way I read it, Prigozhin wanted to stay independent. But not just recently, like over the past ten years or something.
He knew that if this military company was folded in, he would be on the chopping block.
Prigozhin is a siloviki who considers himself to be on the same level as or above the MoD and feels insulted when he receives orders. This is fine usually since his job is mostly doing wetwork in the third world, but when working alongside regular army this is chronically creating clashes. This is exacerbated by the fact his forces got wasted in a stupid engagement for prop reasons in Bakhmut and by other factors, such as Wagner absorbing MoD forces and vice versa.
Stuff that happend in the front were like, Prigozhin doesn't receive enough ammo, so he would absorb MoD squads and send them doing bayonet charges to test ukrainian lines or man trenches that were already filled with the corpses of previous russian squads (according to PoWs).
Prigozhin's behaviour is just prison behaviour. He is a thug, not a james bond villain.
He just vibe checked Putin with the express intent on making him his bottom boy. This is the only scenario that makes sense to me.
Lukachenko mastermind is a scenario I will never buy. Luka is not interested in Wagner nor he is in the war in general. His army is dogshit and specialized in riot control. He doesn't want to commit it, he doesn't want to pay the wages of a PMC.
Luka is a very reluctant participant, and having Prigozhin as a retainer puts a timer on his head.
Wagner attacks from Belarus ? Belarus de facto enters the conflict, which Luka tried his hardest to avoid. Prigozhin throws another tantrum ? Luka falls from a windows and Belarusians clap. This is a shit deal for him, and someone had to call in a favor for it.