[Bug]: Google's dark theme from Google Search Fixer addon is not kept when Desktop site mode is enabled

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Steps to reproduce

1. From Settings > Add-ons, enable Google Search Fixer.
2. Go to google.com.
3. From the bottom on the page, enable the Dark theme (Dark theme: on).
4. Tap the 3-dot menu and enable the Desktop site mode.
5. Observe the theme on the webpage.

Expected behaviour

When Desktop site mode in enabled, the dark theme remains enabled.

Actual behaviour

When Desktop site mode in enabled, the dark theme is replaced by light theme.

Device name

Lenovo Yoga Tab 11

Android version

Android 11

Firefox release type

Firefox Nightly

Firefox version

Nightly 105.0a1 from 08/08.

Device logs

No response

Additional information

Also reproducible on Beta and RC.
https://user-images.githubusercontent.com/89388888/183678028-7a4e5e60-1b44-46f0-b7d4-ddca8e360273.mp4

┆Issue is synchronized with this Jira Task

[delia-pop]

Moved to bugzilla: https://bugzilla.mozilla.org/show_bug.cgi?id=1784005

Change performed by the Move to Bugzilla add-on.