No, changing the winding ratio does not increase "power".
If you put 100 watts into a transformer, you will only get 100 watts out (actually slightly less due to efficiency loss).
But wattage is voltage times current. If I put in 100 volts at 1 amp of current and have a double winding on the second coil, I'll get out 200 volts, but only at 1/2 amp. I'll still have 100 total watts.
If I do the reverse, I'll have an output of 50 volts, but at 2 amps current - still 100 total watts.
Transformers can change voltage but do not magically create extra power.
If you put 100 watts into a transformer, you will only get 100 watts out (actually slightly less due to efficiency loss).
But wattage is voltage times current. If I put in 100 volts at 1 amp of current and have a double winding on the second coil, I'll get out 200 volts, but only at 1/2 amp. I'll still have 100 total watts.
If I do the reverse, I'll have an output of 50 volts, but at 2 amps current - still 100 total watts.
Transformers can change voltage but do not magically create extra power.