fix(vue-router): admin-template route tables, children and layouts; Nuxt routes only in Nuxt (#2130)

vue-element-admin, vue-admin-template and vben had no routes: their tables
are named arrays (`export const constantRoutes = [...]`, `const routes:
RouteRecordRaw[] = [...]`) or per-module objects (`const tableRouter = {…}`)
handed to `new Router(...)`, and most of their screens are `children`.

The Vue Router reader now reads those tables in any file that builds a
router, imports vue-router or lives in a router/ directory; joins children
onto their parent's path (a parent is a screen only when no child claims
its address and it doesn't redirect); binds a lazy view by the FILE it
imports (all of vue-element-admin's are `…/index.vue`), through an alias the
resolver can't follow by the one file in the app with that path; links each
screen to its parents' components as layouts; and takes `this.$router.push`.

Nuxt's file routes move into their own `nuxt` resolver, detected only in a
Nuxt app: halo's plain-Vue console got 30 made-up screens from its `pages/`
folders. A Nuxt app at the repository root now gets its routes, and a
top-level `pages/index.vue` is `/`, not `/index`.

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

docs/design/framework-coverage.md

@@ -40,7 +40,7 @@ guessed.
 | Next.js | `frameworks/nextjs.ts` | `next-router-synthesizer.ts` | `nextjs.test.ts` | next-saas-starter |
 | React Router | `frameworks/react-router.ts` | `react-router-synthesizer.ts` | `react-router.test.ts` | proshop (44 edges) |
 | TanStack Router | `frameworks/tanstack-router.ts` | `tanstack-router-synthesizer.ts` | `tanstack-router.test.ts` | TanStack examples, fastapi-template frontend |
-| Vue Router / Nuxt | `frameworks/vue-router.ts` | `vue-router-synthesizer.ts` | `vue-router.test.ts` | vue-realworld (23 edges) |
+| Vue Router / Nuxt | `frameworks/vue-router.ts` (Nuxt file routes: `nuxtResolver` in `frameworks/vue.ts`) | `vue-router-synthesizer.ts` | `vue-router.test.ts` | vue-realworld (23 edges); vue-element-admin (62 routes), vue-admin-template (14), vben (192), halo console (34) — named tables, module files, `children` + layouts; Nuxt: mealie, elk, nuxt/movies |
 | SvelteKit | `frameworks/sveltekit-router.ts` | `sveltekit-synthesizer.ts` | `sveltekit-router.test.ts` | sveltekit-realworld (31 edges) |
 | Angular | `frameworks/angular-router.ts` | `angular-template-synthesizer.ts` | `angular-router.test.ts` | angular-realworld (31 edges, 18 renders), Ghostfolio (189 edges, 170 renders), ngx-admin (routes and renders; its menus are config) |
 
@@ -191,6 +191,10 @@ Each of these cost real debugging time; they are not hypothetical.
    `name` is written above its `path`, so a text window handed every entry its
    predecessor's name — silently, for every route in the file. Use
    `frameworks/object-literal.ts`.
+   A lazy view binds by the FILE it imports, never by the import's last
+   segment: vue-element-admin's views are all `…/index.vue`.
+   Nuxt's `pages/` convention belongs to a Nuxt app only — a plain Vue app's
+   `pages/` folder (halo's console) holds components a router config names.
 5. **A receiver is required for a generic verb.** `push` and `replace` are two
    of the most common method names in JavaScript; claiming a bare one puts every
    `paths.push('/tmp/x')` one string-match away from a route.