I don't really know, so don't pay much attention to this answer - Is that set-up maybe creating a ground loop which could/would be the source of the distortion/noise?
If the amp and the laptop/'phone don't genuinely share a common ground point/reference that could be the problem you describe of disparate reference voltages between devices.
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Maybe you can incorporate into the stereo amplifier circuit something along the lines of (but not specifically) an optocoupler/isolation amplifier (galvanic isolation)/etc to separate your power supply from the input signal of interest.
Or, and with the little I know, I might have looked into this point first - perhaps design some sort of compatible "enable" feature for the amp power supply when the audio jack is plugged in, or use a device that has this feature to do so, to avoid using the input signal audio jack being mixed in with the power supply 0V line (if that is your design).
if you're using a microcontroller or something, then it should be possible to configure the device to respond to an action (audio jack in), and be on standby/sleep/whatever it's called until that moment, a digital "enable" rather than an analogue version.
I really don't know what you're doing as you posted no schematic which makes it harder to offer (poor or inappropriate) advice, and no doubt am very wrong about this last point, but I suspect that unless it's a PLC (powerline communications)circuit
, then mixing/crossing signal with power is "not recommended" if avoidable.