See, Apple? Even cars can do it :)
That’s like asking who owns a propane tanks for your grill. You own it while you have it.
When you get a new batter, you own the new one, and relinquish ownership of the previous one, paying for the electricity that’s on the new battery. AS LONG AS the battery that you’re relinquishing is substantially identical to the new battery.
Sure. If you’ve abused it in some way so that it doesn’t take or hold charge, then you might have to pay for a replacement battery. But I think there would be an implied warranty when you’re given a replacement, that the replacement was fit for service. And the company might just have to roll the cost or replacing batteries every so often into their electricity pricing models.