"System" using 342GB storage?
The answer was found through a comment by Irfan Latif here: &quot;System&quot; using 342GB storage? While I'd found this question prior to posting my own, I had dismissed it as being inapplicable since my df output is very different, and I hadn't found the menus shown in the screenshots there.

What I had to do is to go to Settings -> Storage -> The (almost empty) SD card. Then click on the grippy 3-dot menu in the top right, and select Migrate. You then get into the menu mentioned in the above answer (which was apparently supposed to show up when first installing the SD card, but didn't show for me). I moved the content, which took 15 minutes or so. And since then my phone indicates:


Internal shared storage: 344GB used of 367GB
SanDisk SD card: 26.32GB used of 361GB


When plugging in the phone, it now also indicates 334GB available space, and I can load more music and take more pictures.

Thank you for the suggestions, everyone.