I have no idea about the circuitry, but the parts used are simple components and I can't see why they don't work. If I had to guess, it would be the SSR, but have you checked its operation by itself?
![Shocked :o](https://www.eevblog.com/forum/Smileys/default/shocked.gif)
In practice, a zero-crossing switch could be achieved by using a diode, a resistor and a capacitor to step down and rectify the voltage, and then inputting the voltage to an SSR.
because the SSR used is a relay that operates at zero crossing.
But after the SSR operates, the circuit has a common mechanical relay operating to bypass the SSR contacts. I don't understand why they are doing this.
Presumably, this product is for audiophiles and was made with a focus on "sound quality".
check to see if the SSR is working properly.