Feature: Reactivate NuxtLayout app shell

[mjkatgithub]

Goal

Reintroduce NuxtLayout as the app shell baseline and prepare clean separation
between public and authenticated layouts.

Scope

• Reactivate NuxtLayout usage in app entry
• Define baseline public vs app layout boundaries
• Remove/resolve current warning about unused layout component
• Keep behavior compatible with future user-customizable layouts (Epic 4)

Branch

feature/nuxtlayout-reactivation

Acceptance Criteria

• NuxtLayout is actively used again in app entry path
• Public and app pages can be assigned to distinct layout baselines
• Existing warning about unused layout component is removed
• No routing/render regression introduced by layout reactivation

Test Checklist

Unit

• Layout selection logic for public/app routes

Integration

• App shell renders expected layout for landing and chat routes
• Warning related to unused layout component no longer appears

E2E

• Visit / and /chat and verify expected layout shell behavior