The problem is that when the switch is configured as an on/off switch, when it’s on, it’s not passing the full sine wave to the load. It has a step, as shown in the image below.
This is a problem because some loads can’t handle that sudden voltage step seen at the center of the image, where it’s basically a flat horizontal line then there’s a vertical jump up to that faint gray grid line. For example, I’m pretty sure that’s what’s causing the transformer buzzing reported in this thread
And the desired outcome is for the switch in on/off mode to pass a smooth sine wave to the load, like the blue trace in the bottom image. If possible, the relay should click to connect the line directly to the load without the dimming circuitry being involved. But if the dimming circuitry is always going to be active, perhaps the MOSFETs could be turned on for more of the time to reduce/eliminate the step.
Switch configured for on/off, relay click is enabled:
