Why when you pull a shield from someone you killed, is it full?

I always figured there was a science-fiction explanation for this. Try to imagine Symmetra's abilities from Overwatch and how they are made of 'hard light'. That is the closest similarity to how I think body shields (and other force fields) work in Apex Legends. Essentially the body shields do not have a true material form and their properties are determined by a computer in much the same way as hard light, but via an advanced system designed for the games which can manage rules remotely. Possibly the same remote system that caps the legends capabilities to reuse their ultimates (which despite being very diverse can all be accelerated using the same vague item) or bring their dead allies back to the battlefield (which is somehow only possible via a banner).

If body shields are completely fabricated from some sci-fi technology then the host of the games can giveth and taketh as they please. So the fact that shields instantly rejuvenate upon the death of the wearer is not just Respawns choice of balancing, but also a choice of the in-world hosts of the Apex games.

This is the assumption that I've had since very early on, and since then they have also introduced evo shields which would make no practical sense in an actual warzone, but still fit with my personal theory. I haven't played the Titanfall games yet (but they are on xbox game pass/ea play so I will soon) but I would not be surprised if I found more stuff that fit from those games.

That's about as far as I'm willing to dig into it though. It would probably compromise on the fun element of the game to force everything make sense. Why do half of the squads all have an Octane? How can the legends die thousands of times over and keep coming back?

Oh you wanted a design explanation. Using batteries after every battle is frustrating, and for shields to not work in this manner would likely enhance the effectiveness of third-partying further.