Add documentation for staging and production environments

[devin-ai-integration]

Summary

Adds a new section to the "Publishing your docs" page explaining how to set up separate staging and production documentation sites. This addresses a common customer workflow where teams want to preview changes on a staging site before publishing to production.

The new section covers:

• Configuring multiple instances in docs.yml (with the important note that URLs should not include https://)
• Using the --instance flag to publish to a specific environment
• GitHub Actions workflows for auto-deploying to staging and manually deploying to production

Updates since last revision

Enhanced the GitHub workflow examples based on a real customer implementation:

• Added workflow_dispatch trigger to staging workflow (allows manual triggering in addition to auto-deploy on push)
• Added fern check validation step before deploying to catch configuration errors early
• Renamed job from run to deploy for clarity

Local Testing Completed

• Ran fern docs dev locally and verified the new section renders correctly
• Steps and Accordion components display properly
• Code blocks have correct syntax highlighting
• Visual verification confirmed all formatting is professional and consistent

View original video (rec-1609bf99d0c94acea32f96d3896545fa-edited.mp4)

Review & Testing Checklist for Human

• Verify the --instance flag syntax is correct (e.g., fern generate --docs --instance plantstore-staging.docs.buildwithfern.com)
• Confirm that instance URLs in docs.yml should NOT include https:// - this was a key issue discovered in customer support
• Test the GitHub Actions workflow examples are valid YAML and follow best practices
• Preview the rendered documentation to ensure the Steps and Accordion components display correctly

Recommended test plan: Run fern docs dev locally and navigate to the Publishing your docs page to verify the new section renders correctly with proper formatting.

Notes

• This documentation is based on a customer support thread where the https:// prefix issue caused publishing failures
• Workflow examples updated based on a real customer's staging/production setup
• Uses "plantstore" as the example organization to match existing examples on the same page
• One pre-existing Vale error remains on line 182 (in content not modified by this PR)

Link to Devin run: https://app.devin.ai/sessions/26b48e26643b41edb363c03490d64994
Requested by: Danny Sheridan (@dannysheridan)

[devin-ai-integration]

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🌿 Preview your docs: https://fern-preview-7ec860a2-9ed0-469a-bd98-3e2c75680089.docs.buildwithfern.com/learn

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🌿 Preview your docs: https://fern-preview-02576607-1559-46b5-a5e3-ec443d99c95b.docs.buildwithfern.com/learn

[github-actions]

🌿 Preview your docs: https://fern-preview-c4d24053-1c3f-4d7b-b600-a44f24e05496.docs.buildwithfern.com/learn