Fix 404 error on public profile when all user domains are private

[ALeonard9]

Story

As a druthers user with private domain shelves, I want my profile endpoint /v1/public/{handle} to return 200 with an empty/private profile payload instead of 404, so visitors see my profile header and private state instead of a Page Not Found error.

Acceptance Criteria

• /v1/public/{handle} returns HTTP 200 with profile header and private state indicators when all domain permissions are private.
• Non-existent handles continue to return HTTP 404 Not Found.
• druthers-web handles 200 private state response without triggering Next.js notFound().

Context

Raw capture: By default, if you have a public profile, you should display your top 5. BUG: If you have all domains private, you get a 404.

Channel Impact

• Web: companion ALeonard9/druthers-web (profile page top 5 & private state rendering)
• iOS: no impact — handles 200 response with private state flags naturally
• MCP: no impact — MCP profile lookup tool handles private status on 200

Estimate

• Recommended model: Sonnet 5 — routine API logic and error handling update
• Human effort: S — quick code review and verification of profile page rendering