docs: Move openai and slack to developers/build/connectors/integration/*

[royendo]

Two things, is it integrations? and this might be confusing with the developers/integrate but Verb vs Noun/ different levels should be ok.

Checklist:

• Covered by tests
• Ran it and it works as intended
• Reviewed the diff before requesting a review
• Checked for unhandled edge cases
• Linked the issues it closes
• Checked if the docs need to be updated. If so, create a separate Linear DOCS issue
• Intend to cherry-pick into the release branch
• I'm proud of this work!

[ericpgreen2]

Naming: "Service Integrations" instead of "External Integrations"

"External" is redundant since all connectors connect to external systems. The key distinction is that OpenAI and Slack enable features rather than import data. "Service Integrations" captures this better and is extensible for future additions (Teams, PagerDuty, other AI providers, etc.).

Changes needed:

• connectors.md line 265: Change section header to "Service Integrations"
• integration/index.md: Update title to "Set Up Service Integrations", sidebar_label to "Service Integrations", and revise the intro text (e.g., "Service integrations connect Rill to third-party platforms that enable features like AI-powered analytics and notifications.")

Directory path: /services/ instead of /integration/

Since this hasn't shipped yet, let's pick the right path from the start. Recommend renaming the directory from integration/ to services/ so the URL is /developers/build/connectors/services/. This matches the "Service Integrations" label and reads naturally under /connectors/.

This will require updating all the new paths in connectors.md, alerts.md, project-errors.md, guide/alerts/index.md, and the redirect rules in docusaurus.config.js.

Inconsistent Slack icon class

In connectors.md line 282, the Slack icon uses className="sheets-icon", but the new integration/index.md correctly uses className="slack-icon" (which was added to _connector-icon.scss). Update connectors.md to use slack-icon as well.

Minor

• integration/index.md line 23: "a OpenAI" → "an OpenAI"
• Consider adding a _category_.yml file to the new directory for consistency with data-source/ and olap/

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Developed in collaboration with Claude Code