fix: add NEXT_PUBLIC_ADMIN_URL to web deployment for Better Auth trusted origins

[saddlepaddle]

Fixes Better Auth trusted origins error in web app by adding NEXT_PUBLIC_ADMIN_URL to the deployment workflow.

The auth package requires all 4 URLs in trustedOrigins: WEB, API, MARKETING, and ADMIN. The web deployment was missing ADMIN_URL, causing Better Auth to reject it as an invalid origin.

This completes the full fix across all apps:

• PR fix: add NEXT_PUBLIC_MARKETING_URL to API deployments #644: API deployment
• PR fix: add NEXT_PUBLIC_MARKETING_URL and NEXT_PUBLIC_ADMIN_URL to marketing/admin deployments #645: Marketing and Admin deployments
• This PR: Web deployment

Summary by CodeRabbit

• Chores
  • Updated deployment configurations to propagate admin environment variables across preview and production environments for all services.

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[coderabbitai]

Caution

Review failed

The pull request is closed.

📝 Walkthrough

Walkthrough

The pull request adds NEXT_PUBLIC_ADMIN_URL environment variable propagation to both preview and production deployment workflows. This variable, derived from ADMIN_ALIAS, is exported globally and passed through vercel deploy commands for the API, Web, and Docs pipelines.

Changes

Cohort / File(s)	Summary
GitHub Actions Deployment Workflows .github/workflows/deploy-preview.yml, .github/workflows/deploy-production.yml	Added NEXT_PUBLIC_ADMIN_URL environment variable to global env blocks and propagated through vercel deploy commands across API, Web, and Docs deployment steps. No control-flow modifications.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Possibly related PRs

• #509: Adds NEXT_PUBLIC_API_URL propagation to the same workflow files following an identical pattern
• #345: Similar environment variable additions to deploy workflows with vercel deploy command wiring

Poem

🐇 A new URL hops into view,
NEXT_PUBLIC_ADMIN travels through,
From preview to prod, it takes flight,
Vercel commands beam it just right! ✨

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📜 Recent review details

Configuration used: defaults

Review profile: CHILL

Plan: Pro

📥 Commits

Reviewing files that changed from the base of the PR and between 645f486 and b9e41d1.

📒 Files selected for processing (2)

• .github/workflows/deploy-preview.yml
• .github/workflows/deploy-production.yml

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[github-actions]

🚀 Preview Deployment

🔗 Preview Links

Service	Status	Link
Database (Neon)	✅	View Branch
Electric (Fly.io)	✅	View App
API (Vercel)	✅	Open Preview
Web (Vercel)	✅	Open Preview
Marketing (Vercel)	✅	Open Preview
Admin (Vercel)	✅	Open Preview
Docs (Vercel)	✅	Open Preview

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