Is it voltage or power of the signal amplified when the opamp amplification is given in dB unit?
No, voltage gain is 20 log the ratio and not 10 log the ratio.

20dB = voltage gain of 10 and a power gain of 100. For the op-amp circuit it only makes sense to set it to have a voltage gain ratio of ten

Voltage gain = 20\$log_{10}(\dfrac{V_O}{V_I})\$ or 10\$log_{10}(\dfrac{V_O}{V_I})^2\$ = 10\$log_{10}(\dfrac{P_O}{P_I})\$

Just think about the power in a resistor if you made the voltage ten times bigger, the power goes up by the square of the voltage increase.