Cleaner music when laptop is on battery vs plugged in

I would hazard a guess that when you use it from battery you are not getting all the and RFI from the mains supply.

Laptops are notorious as the worst possible devices to use in Computer Audio, for the very reason cited. May I suggest, as a very inexpensive alternative, using a Raspberry Pi computer with a digi+ S/PDIF card, and eliminate the laptop.

Make sure your USB cable from the PC to the DAC has a ferrite core at the PC end, and even better, both ends.

It’s well-known that a laptop is a noisy source. More noise gets added when powered by an AC/DC wall wart - which is a cheap switch-mode power supply. Running on the battery is far better but doesn’t last long. A quieter option is to get a regulated linear power supply (LPS) - something like this one - and plug it into a power conditioner/filter. Find out what DC voltage your laptop uses.