Internally work with modern config syntax for template binary sensor platform config

[balloob]

Breaking change

Proposed change

This makes the binary sensor internally work with a modern config syntax. This is a requirement to add trigger support.

Aligns config set up with #48976

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Example entry for configuration.yaml:

# Example configuration.yaml

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• This PR fixes or closes issue: fixes #
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[balloob]

If tests fail, they will pass after rebasing on #49094 Rebase done

[balloob]

@MartinHjelmare I have also removed the modern config syntax from the platform config here.

[MartinHjelmare]

Looks good!