Rustdoc does not update the stored theme if the currently displayed theme matches the system

[Nemo157]

Repro:

• Clear local-storage for doc.rust-lang.org
• Set system theme to light
• Visit https://doc.rust-lang.org/stable/std/ and change theme to ayu
• Visit https://doc.rust-lang.org/nightly/std/ and note that the theme has been set to light following the system
• Visit https://doc.rust-lang.org/stable/std/ and see that the theme changes back to ayu because the stored theme was never updated
• Visit https://doc.rust-lang.org/nightly/std/ and then change the system theme to dark, updating the displayed theme to ayu, and then change the system theme back to light, updating the displayed theme to light
• Visit https://doc.rust-lang.org/stable/std/ and see that the theme is now light because the stored theme was updated

This affects the plan we have for docs.rs to follow rustdoc's theme setting, rust-lang/docs.rs#1116 (comment), I assumed that rustdoc would update the stored theme whenever it changes so we could synchronize off that. Missing the initial setting based on the fact that light is the "default" theme loaded before the JS runs seems like a bug.

cc @nasso,

[rustbot]

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[nasso]

I assumed that rustdoc would update the stored theme whenever it changes so we could synchronize off that.

I'll implement this 👍