Yup, it's specific to Android 13 (tracked in
https://github.com/koreader/koreader/issues/9446).
This is currently stalled because none of our Android contributors have an affected device

.
The release of LineageOS 20 should help with this (i.e., once I update my own device, I'll finally be able to look into it. Since said device is my daily driver, I'm waiting for the dust to settle a bit on the point release (and, also, to find the time to do the whole backup + migration/update dance

).