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.
In the Tucker interview he said something to the extent of Russian propaganda is no match for American propaganda. Him saying CIA did it would be turned in to a meme in 2 mins. Him not saying anything, regardless if the CIA was involved or not may prove to be better PR in the long run.