Why was TP supposed to steal the Plutonium-241 on behalf of Sator and then lose it? Was it because Sator might be unable to steal it on his own (as Priya said he was supposed to have succeeded in getting the plutonium)? Was it to make sure Sator gets it? And if Sator was able to steal it on his own, why would he allow TP to do it for him which might sabotage his mission (Even if he was going to perform the temporal pincer, why risk it)?

I am trying to wrap my head around this. If TP knew from Sir Michael Crosby that there was a detonation in Stalsk-12, it means he knew where the dead drop was. So why not let Sator steal it, if he failed then good for us and if he succeeded then go to Stalsk-12 to get the fully assembled algorithm.

Priya wanted TP to steal it and lose it so that Sator assembles the algorithm in one place. Priya could have directly talked to Michael Crosby to know about Stalsk-12. OR after knowing about the Stalsk-12 and the algorithm, TP could have figured out the dead drop.

I know that in Tenet, things should happen as they have already happened. This might be a chicken and egg situation. But still, please help me understand this.