I just can't see why Putin would have him killed. It makes no sense to me, he was already in prison, why make him a martyr now, before elections? As an idea elections in Russia are this month.
We also know Tucker interviewed him shortly before Navalny died and we know that Navalny chose to be in Russia. Maybe CIA wanted to not allow people to process the interview and move to martyr Navalny. There are some spicy stuff in the interview like the US blowing Northstream pipeline and Nazis in Ukraine so who knows.
Every media and politician is 100% sure Putin killed him without even considering any alternative.
My take is that the CIA killed Navalny in order to start unrest before elections or to make sure normies keep funding Ukraine.
Though one corollary of that is to effectively run such a place, you need to be seen by those types as the meanest bastard in the room. Even where he doesn't have someone killed he probably wants people imagining he did have that person killed, but with plausible deniability for everyone else.