Migrate backend from vps.goosebumps.fm subdomain to goosebumps.fm/api

[guidefari]

Context

Currently the backend runs at vps.goosebumps.fm. This issue tracks evaluating and potentially migrating to goosebumps.fm/api.

Tradeoffs to consider

Staying on subdomain (vps.goosebumps.fm)

• Independent deploys without touching main domain routing
• CORS already solved
• Easy to add more backend services as separate subdomains

Moving to path prefix (goosebumps.fm/api)

• Same origin = no CORS, cookies just work without credentials: 'include'
• Simpler DNS (one record)
• Cleaner URLs for clients

Work involved

• Update DNS / reverse proxy config
• Update all frontend VITE_VPS_BASE_URL references
• Update CORS configuration
• Update any hardcoded URLs in docs, emails, etc.

[linear]

OPS-94