docs: integrate Elastic CLI into existing API guides

[eedugon]

Summary

• Integrates the Elastic CLI into existing documentation through contextual links and short descriptions where useful.
• Adds CLI references to Cloud and self-managed tool catalogs and to Cloud API workflow pages.
• Registers the cli repository for cli:// cross-repository links.

Dependencies

This PR must not be merged until both of these PRs are merged:

• elastic/docs-builder#3416
• elastic/cli#624

Related to elastic/docs-content-internal#1154.

Validation

• Vale reports no new issues on the changed lines.
• git diff --check passes.
• docs-builder resolves all added cli://index.md links.

Generative AI disclosure

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

• Yes
• No

2. Tool(s) and model(s) used: Cursor with GPT-5.6 Sol.

Made with Cursor

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🔍 Preview links for changed docs

• deploy-manage/deploy/elastic-cloud/manage-deployments-using-elastic-cloud-api.md
• deploy-manage/deploy/elastic-cloud/manage-serverless-projects-using-api.md
• deploy-manage/deploy/elastic-cloud/tools-apis.md
• deploy-manage/deploy/self-managed/tools-apis.md

[github-actions]

✅ Elastic Docs Style Checker (Vale)

No issues found on modified lines!

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