docs: clarify health check docs and sync operator intro

[aantn]

Summary

• Remove "You Can Also:" prefix from deployment-verification heading
• Sync operator intro text across all three pages (README, main docs index, operator index) using the same "Most AI agents" framing
• Move operator section above the terminal GIF on the main docs page so it's the first thing visitors see

https://claude.ai/code/session_01FoAqz3t5mZoEYEbJMurnoW

Summary by CodeRabbit

• Documentation
  • Updated Operator Mode section with expanded descriptions of background operation capabilities, Slack messaging, and GitHub integration features.
  • Added documentation links for Deployment Verification and Scheduled Health Checks.

[claude]

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[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 12041403-062a-4b02-92e0-be88f56d7157

📥 Commits

Reviewing files that changed from the base of the PR and between 4b7d2aa and 6170955.

📒 Files selected for processing (1)

• docs/index.md

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Walkthrough

The documentation homepage (docs/index.md) updates the Operator Mode section with expanded introductory text describing continuous background operation, Slack messaging, GitHub integration, and data source query capabilities. Two feature links—"Deployment Verification" and "Scheduled Health Checks"—are added.

Changes

Cohort / File(s)	Summary
Documentation Update docs/index.md	Expanded operator feature section with additional descriptive copy and new feature links; removed previous section version and omitted "Not just Kubernetes" bullet.

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~3 minutes

Possibly related PRs

• docs: add deployment verification pattern to health checks #1835: Makes overlapping documentation changes to operator landing content with reframing as 24/7 offering and adds identical feature links ("Deployment Verification" and "Scheduled Health Checks").

Suggested reviewers

• Sheeproid
• arikalon1
• pavangudiwada

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately reflects the main changes: clarifying health check documentation and synchronizing operator introduction text across documentation pages.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

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