Figure 03, our 3rd generation humanoid robot

I don't understand why this even has to charge at all. It makes sense for multiple reasons to give it 3 batteries that say have 1/3 of the capacity, and make at least 1, if not 2 or 3 capable of charging independently on a station.

Then the robot would just go to its station and swap its own batteries. Why even have wireless charging at all? Or even a cable? Or even have it "charge"? Battery swapping seems to make way more sense here. Am I missing something?

Bonus points if the robot has data on the degradation and can order its own replacement batteries, take them out of the box, and ship the old ones to a recycling facility...

More bonus points if the charging station is actually outside under a 1KW solar array pergola thing, that way you don't even have to pay for the electricity either. Don't worry, the robot will lock the door when it goes out to grab its batteries. It'll also bring in the whole setup if the weather isn't great.

It depends on the battery life. If the robot lasts all day, then charging at night via standing on a charging pad makes a lot of sense. Creating a removable battery pack adds extra weight and gives the designers less freedom to place the battery pack exactly where it needs to be in the robot frame, or distribute the cells across the frame in strategic locations.

Also, the charge rate matters. If robot can charge to 80% in say 30 minutes, then it can take small charging breaks during the day between critical tasks.

Also, if the feet have inductive chargers, it's possible to place the robot on a large charging mat that allows it to run indefinitely, like in a factory environment. If your robot takes 30 minutes to fold the laundry or do dishes, why not place a charging mat at these locations so it can work and charge at the same time.

In the future, new homes might include charging coils embedded in the floor every 12 inches so that your robots can work all day.

Almost all of those points are applicable for the battery pack as well. There should be virtually no weight difference, other than the design limitation which is a valid concern.