It could still be the batteries but at this point you need to isolate some variables. The batteries appear to discharge fairly quickly (it should last more than an overnight, unless it is being used heavily). It doesn't sound like your phone is recharging the battery either. So you may have a bad battery, a short that is draining your battery or a charge circuit that doesn't charge...or it could be any combination of the three.
If you have access to another phone, try putting a "bad" battery there to see if it will charge and work normally. Likewise, you can take a known-good battery from another phone and put it in the suspect phone to see if it takes a charge. Always use genuine cables and charging bricks.
If the problem is related to the phone, then it may be a bad Lightning port but it could also be a defective charging circuit. You could always use the Lightning port from another phone rather than ordering a new one.
If the charge circuit is bad, that will require a micros-soldering repair.