Remove obsolete hang.now staging deployment

[kixelated]

Changes

• Remove the obsolete hang.now staging environments from both Cloudflare Worker configs and the native staging config.
• Make just deploy target live explicitly for the API, database migrations, and site.
• Update deployment documentation and Worker environment types.

Validation

• bun run check passed (one existing Biome warning in app/src/components/updater.tsx).
• bun run build and bun vite build --mode live passed.
• API and site Wrangler live dry runs passed.

The requested live publish is pending a normal Cloudflare Wrangler login on the deployment host.

(written by GPT-6)

[coderabbitai]

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Run ID: f0034220-ad05-4d8c-b9ad-800c3b16983e

📥 Commits

Reviewing files that changed from the base of the PR and between e36de95 and 69027b7.

📒 Files selected for processing (8)

• README.md
• api/justfile
• api/worker-configuration.d.ts
• api/wrangler.jsonc
• app/justfile
• app/wrangler.jsonc
• justfile
• native/tauri.staging.json

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