Speakers not muted when switching to headphones on X570 Aorus Pro (Realtek ALC1220)

I have a setup with headphones and speakers connected to the same PC (headphones in the front panel, speakers in the rear Line Out jack), and I want to be able to switch between them in software. However, when I switch the output to headphones in my volume mixer (plasma-pa, running through pipewire-pulse), the speakers continue playing alongside headphones. I'm not sure if this is a Pipewire bug or an ALSA one, but let's start here.

I've uploaded pw-dump outputs for both configurations to my web server here: https://static.0upti.me/