I've played with the circuit a little in LTspice. It is a class D amplifier - if we're being polite and not calling it names.
It varies not only the pulse widths, but also the frequency.
When CV is at a higher voltage, the frequency goes down. The frequency in simulation varied from way over 100kHz to 22kHz. The closer CV is to Vcc, the lower the frequency. If CV is pinned up to Vcc by the transistor circuit, then the frequency could be even lower.
I think your transistor amplifier is messed up, so that CV stays way up close to Vcc all the time.
Remove the transistor, and couple V1 in through just C1, and I think you'll get much better results.
You might also need to attenuate the audio signal somewhat.
It's also possible that you are getting aliasing. I don't know how well LTspice converts signals to .wav files, but if the 555 frequency is above the Nyquist frequency for the sampling rate, then you might be getting the switching frequency aliased down in to audible frequencies.
I reconstructed your entire circuit, including the BC107. That caused the switching frequency to drop to about 7kHz. The amplifier or the BC107 model is messed up - and I think it's the amplifier.
I added a capacitor between the collector of Q1 and CV, and the switching frequency went back up to where it belongs.
I think you'll find the squeal is gone with that small modification.
Regardless, this is a lousy "amplifier."