@azzy9 Turning off once the charger is unplugged and it's at "100%" is a typical symptom of a faulty battery.
You can try calibrating it by letting it run down to 0% and charging it fully to 100%, but in my experience with dead batteries it doesn't change anything.
It usually only works for batteries which work for a while and show that they're half full before abruptly reaching 0% and turning the device off. Yours isn't doing that.
As long as the battery model is the same, minor differences in voltage is not an issue. As long as it's within 10%, it's perfectly fine.
I would go ahead and replace the battery.