confused about power

Hi, that looks like a really nicely built project!

From what I can see, you're using relay modules which have all the drive electronics inside. The only gotcha I've found with those is that often they have pullup resistors that pull the inputs up to whatever voltage you're powering them from (in this case 5v). But because you're using a shift register (which I guess is also running off 5v) you should be fine.

How is the Pico being controlled? Is it from the switches in the final box? It might be that the long wire to the end box is actually picking up noise caused by the spark from the relays (I've had this happen).

There are some things that might help:

• Try a much shorter black cable to the white box. You could also try finding/making a cable that has a ferrite in it (that chunky bit of plastic a few inches from the end).
  
• If you have pullup resistors in the final white box, lower their values. Something like 1k is probably beefy enough. You could also put small capacitors across the wires in the box with the Pico.
  
• To properly isolate the Pico from the mains, you could add an opto-isolator chip inside the adaptor. Since you won't have many wires to the shift register, it should be pretty easy to do - and then you don't have to share GND at all.
  
• Other thing is to find blocks of 'solid state relays' - they're available in a similar form to the relay modules you have, but because they are semiconductors you don't get the spark when they open and close, which means less noise.
  
  

But yes: Sharing GND between different voltages should be fine - I'm not sure you'll notice much of a difference when powering from a battery though.