[Light Switch] Fix Light Switch start up logic (#45304)

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## Summary of the Pull Request
Title

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## PR Checklist

- [x] Closes: https://github.com/microsoft/PowerToys/issues/45291
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- [x] **Communication:** I've discussed this with core contributors
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## Detailed Description of the Pull Request / Additional comments
Before, there was a function that initialized some variables about the
current system state that were later used to check against if that state
needed to change in a different function. That caused from some issues
because I was reusing the function for a double purpose. Now the
`SyncInitialThemeState()` function in the State Manager will sync those
initial variables and apply the correct theme if needed.

I also removed an unnecessary parameter from `onTick`

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## Validation Steps Performed
Manual testing