Here I have my batteries connected in series and then have them plugged into a power switch from can I charge the batteries through the switch like I have in the photo or do I have to unplug them every time
I don’t think you can do that. that little board you have there is not a switch, its a couple of FETs that get saturated when you press the power button. the current flow through the FETs is one way. Its not designed to work the other way.
if it was a dumb switch it would work.
Better off unplugging it and balance charging the batteries.