Follow-up to #61079, #61236, #63830, and #63847.

Same symptoms as #63830. Additionally, I'm seeing styles from both light.css and dark.css active, and the ones in light.css are taking precedence over the ones in dark.css even though the system is in dark mode. Tested on https://doc.rust-lang.org/nightly/std/ after deleting the local storage entry, and docs generated locally.