The datasheet shows that An LM386 works well with a 6V or 9V supply. It shows that with a 12V supply its output power is not increased much but its heating increases a lot.
Yours is in a socket instead of being soldered to the copper traces on the circuit board. The copper traces help carry heat away when it is soldered to them.
With a 6V supply, the output voltage swing into an 8 ohm speaker at clipping is 4V peak-to peak which is 0.25W. Its heating is 0.22W.
With a 9V supply, the output voltage swing into an 8 ohm speaker at clipping is 6V peak-to peak which is 0.56W. Its heating is 0.52W.
With a 12V supply, the output voltage swing into an 8 ohm speaker at clipping is 6.5V peak-to peak which is 0.66W. Its heating is 0.82W.
Its maximum allowed heating when it is not enclosed and is in 25 degrees C air is 1.25W when it is extremely hot (150 degrees C inside it).
You measured its current as 190mA when driven lightly then its total power is 12V x 190mA= 2.28W. Then its output power and heating are much more than shown on the graph in the datasheet so it is probably oscillating. At clipping its total power is 0.66W + 0.82W= 1.48W. Then its current is 1.48W/12V= 123mA.