Why such large error on Tinkercad opAmp in my setup?
I think you have misunderstood the specifications for your op-amp. The NE5532 is only guaranteed to provide at least 10mA under short-circuit conditions. That's the worst-case value. You should never design assuming "typical" behavior.

Furthermore, the "short circuit current" specification is measured with the output shorted to ground. In other words, if you try to draw the specified short-circuit current from the op-amp then the output voltage is zero. You can't expect to get that much current at any output voltage greater than zero.

The specification you should be looking at is output swing if you look at these numbers you will see that this op-amp is typically used with output currents around 5mA or less.

There are many ways to boost the current from an op-amp. In this case, I think it would be better to look for a device or circuit that is specifically designed to charge your LiPo cell.