Updates "Using the API" page so it matches how developers look up Kibana Security APIs

[nastasha-solomon]

Summary

Updates Using the API (solutions/security/detect-and-alert/using-the-api.md) so it matches how developers look up Kibana Security APIs, which is by searching for literal strings (path segments, group slugs, and doc paths) instead of long marketing-style link labels.

Fixes #5797

Changes

• Intro cross-links — Replaced verbose titles (“Security detections API (Serverless)”, etc.) with short, searchable literals: the OpenAPI group slug endpoint-security-detections-api for Stack and Serverless, and the docs path solutions/security/apis for the broader Security APIs page.
• Layout — Reorganized around ## API endpoints with subsections (Detection rules, Detection alerts, Exceptions and lists), similar to the APIs and tools pattern (Endpoint / function-style tables).
• Tables — Three columns: Function | {{stack}} | {{serverless-full}}, with the same endpoint literal in each deployment column pointing at the correct Stack vs Serverless Kibana API reference.
• Link text — Uses path-style names developers type or search for (for example detection_engine/rules, detection_engine/rules/_find, exception_lists, lists), not full METHOD /api/... strings or generic “Stack” / “Serverless” labels.
• Presentation — Tables wrapped in :::{table} with column width hints so the layout stays readable.

Why

External developers often find APIs by pasting part of a path or slug into search. Aligning visible link text and headings with those literals makes the page easier to scan and matches the mental model they use in the API docs and in code.

Generative AI disclosure

1. Did you use a generative AI (GenAI) tool to assist in creating this contribution?

• Yes
• No

Cursor + Composer 2 max

[github-actions]

🔍 Preview links for changed docs

• solutions/security/detect-and-alert/using-the-api.md

[github-actions]

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[mdbirnstiehl]

APPROVED!