MacBook shows Power Source as Power Adapter even when unplugged
I had this issue once, SMC reset didn't help neither nor turning the option off and on again...
What I did was:

I turned off my MBP without beeing connected to a power source
I connected it and waited until the charging logo appear
I turned it on still connected

After that, it came back to normal
(I noticed this bug when I was looking at the istat menu battery log while pluggin/unpluggin the power source)