Try both sides of the USB-C. What do I mean? Unplug the cable, flip it over and plug it in again. Each USB-C jack has two distinct charging circuits, top side and bottom side. Because it doesn't charge on one side doesn't mean it won't charge on the other. If you flip over the cable and still get 5V with 70ma, try a different USB port and test both sides on that port. MBP can charge from any USB-C on either side.
If still not charging, disconnect the battery and check readings again. A bad battery can prevent the USB-C control chips from turn on to 20V. That 5V signal is the test signal, once the charging circuit and battery circuit give an AOK, that voltage will jump to 20V.
Edited to say 20V, I've been fixing USB-C on Nintendo switches for two days and they charge at 15V.