The idea was, that you have a look into a textbook to see, how OPamps are stabilized.

I cannot recall the whole theory here, but the main principles are as follows:

Normally the power amplifier is internally compensated to be stable at unity gain. This means, its open loop gain falls at a slope of 20db/decade by the help of an internal first order low pass filter. In the schematic you will mostly see a small cap somewhere at some driver stage providing this.

The consequence is, that this cap causes a phase lag between output and inverting input of about 90°. So, no more than 90°C must be generated additionally by the load and feedback parts, otherwise the total loop phase shift reaches 360° and the OPamp begins to oscillate.

But because the phase lag between output and inverting input is unsanely influenced by stray capacitance at output and the phase lag increases at highest frequencies due to the finite signal travel time within the power amp, a certain well dosed phase lead should be introduced by connecting a suited capacitance from output to inverting input.

So, this answers your question: Adding additional low pass filtering within the loop increases the phase lag and makes your application to become unstable or even to oscillate. What you need is the introduce of a suited phase lead!

You can add a low pass filter, but only to the noninverting input, where you input the sine.

Your power amplifier should not be too fast. A loop gain of about 20dB at the highest frequency of interest should be enough. (Remember: Open loop gain / closed loop gain = loop gain)

Kai