You will only get voltage drop and under-reading if significant current is drawn down those same wires OR there was a wiring issue causing high resistance (volts equals current times resistance). A 1V drop between battery and accessories plug without load would be of concern.
Both multimeter and plug voltmeters are cheap so it is easy to check. Just make sure to get ones which state the accuracy.
You should be sitting at between 13. 8 and 14.2V when the car is running. Too high means the alternator regulator is bad and you will boil dry your battery (plus possible electrics issues), too low and the battery will not charge properly. It may be a little low at idle and/or immediately after starting, ideally test across a range of rpm.
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