DOCS-11615: Improve Azure App Services logging documentation (#30685)

* Improve Azure App Services documentation and reduce code duplication

- Enhance logging documentation for Azure App Services across .NET, Java, and Node.js
- Create reusable partials and shortcodes to eliminate ~150 lines of duplicated content
- Fix broken relative links in Programmatic Management section
- Convert internal Datadog links to use absLangURL for proper multilingual support
- Move link references inside tabs for proper scoping
- DRY up Custom Metrics and Logging sections with language-specific content
- Maintain external links as direct URLs for third-party services

This significantly reduces maintenance burden by centralizing common content while preserving language-specific guidance.

* refactor

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Co-authored-by: cecilia saixue watt <[email protected]>

Author: petems