docs(router): add examples of API routes

[deepakrudrapaul]

PR Checklist

Please check if your PR fulfills the following requirements:

• The commit message follows our guidelines: https://github.com/analogjs/analog/blob/main/CONTRIBUTING.md#-commit-message-guidelines
• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)

PR Type

What kind of change does this PR introduce?

• Bugfix
• Feature
• Code style update (formatting, local variables)
• Refactoring (no functional changes, no api changes)
• Build related changes
• CI related changes
• Documentation content changes
• Other... Please describe:

Which package are you modifying?

• vite-plugin-angular
• vite-plugin-nitro
• astro-angular
• create-analog
• router
• platform
• content
• nx-plugin
• trpc

What is the current behavior?

Closes #599

What is the new behavior?

Does this PR introduce a breaking change?

• Yes
• No

[optional] What gif best describes this PR or how it makes you feel?

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[brandonroberts]

Thanks! @allcontributors add @deepakrudrapaul for doc

[allcontributors]

@brandonroberts

I've put up a pull request to add @deepakrudrapaul! 🎉