If you are buying PlayStation earbuds you might as well buy 2 more dual sense Controllers so you always have one fully charged ./s (though I wouldn't be surprised if some middle level exec at Sony is thinking exactly this)
That's in the back of the controller. If you open a dual sense you'll see that the "only" thing that would be in the way of the charger is the battery.
The DualSense successor would feature a charging case-like compartment in the back where you can place your earbuds and charge them.
This article explicitly states where Sony wants to put the charger. Illustrations done to drive article views are not a good replacement to actually reading the text.