Prepare admin app for Vercel deployment

[IgnazioDS]

Summary

• add a real Next.js ESLint setup for the admin app
• harden admin cloud env validation and proxy runtime config for Vercel
• document the Vercel root-directory and env setup for apps/admin

Verification

• npm run lint
• npm run build

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Apply fallback after sanitizing CLOUD_BASE_URL

Select the fallback only after normalizing CLOUD_BASE_URL; with the current process.env.CLOUD_BASE_URL || process.env.NEXT_PUBLIC_CLOUD_BASE_URL order, a whitespace-only or quote-wrapped empty CLOUD_BASE_URL is treated as present and prevents fallback, causing startup to fail even when NEXT_PUBLIC_CLOUD_BASE_URL is valid. The prior implementation trimmed before ||, so this is a behavior regression for misconfigured-but-recoverable env setups.

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