I just discovered with my iPhone 11 Pro Max that the phone AND the Apple battery case seem to be charging when together and the power cord is only attached to the case.
Last week I noticed I could charge the battery case independently of the phone and vice versa. Each could fully charge (plugged in). The case while charging displayed an orange light and when fully charged changed to green.
As evident from all the posts it seems the phone is being charged and not the battery case. Indeed my 11 is showing 100% charged all the time. Yesterday my phone was used quite a bit and habit made me recharge the phone in the battery case over night. I thought, idiot, you know there’s a problem!” I removed the phone from the case, plugged in the case only and found to my joy, the charging light was green! I repeated the experiment with the same result.
if you have an 11 PRO MAX and the genuine Apple battery case give it a try. I will report back if anything changes. If both can simultaneously charge consistently then it is a software bug for this iPhone combo. I cannot speak for other iPhones/battery case combinations.
Good luck and I hated removing the phone all the time and smudging my camera lens!