OK, then it looks like it's not a hum loop, as there's no connection between the systems.
Your description of the effect varying as you touch things suggests that it's an electromagnetic pickup thing, and you are acting as an antenna.
There's one thing in your post that was a red flag, and I'll come to that.
So yes, the laptop PSU seems to be a bit noisy and is radiating 50Hz.
And you are it's antenna.
You could try another PSU, it could be faulty. Is it genuine?
On the other hand, it could be the sound system is being over-sensitive to 50Hz in the air.
The thing that raised a red flag was you saying you were connecting a headphone output to a phono input.
That word 'phono' can be used to mean two different things.
Some people use it to describe the type of connector: the RCA/Phono jack.
But it can also mean the name of the input on the amp.
On the back of the amp, there will be a bunch of different inputs: Phono, CD, Tuner, Tape, Aux etc etc.
They will all have the same RCA/Phono jacks as input.
But an input labelled 'Phono' is different from the others: it's super-sensitive and is designed for a vinyl pick-up cartridge. It's expecting a few millivolts.
All the others are 'line level', and are expecting a signal of up to a volt.
You should not be feeding a headphone-level output into a input labelled 'phono'.
That's going to hideously over load it, and the input may also be sensitive enough to pick up 50Hz noise because it's not properly terminated into a low-impedance cartridge coil.
Connect a headphone output to any of the other amp 'line level' inputs.