Refactor docs to use Nuxt Content v3 and file-based pages

Migrates documentation from markdown-based content to Nuxt Content v3 with file-based routing. Removes old markdown content files, adds new Vue page components, updates layout and content rendering logic, introduces a Prose wrapper, and updates dependencies for Nuxt Content v3 and related packages.

docs/content.config.ts

@@ -0,0 +1,19 @@
+import { defineContentConfig, defineCollection } from '@nuxt/content'
+import { z } from 'zod'
+
+export default defineContentConfig({
+  collections: {
+    guide: defineCollection({
+      type: 'page',
+      source: 'guide/**/*.md',
+      schema: z.object({
+        section: z.string().optional(),
+      }),
+    }),
+
+    api: defineCollection({
+      type: 'page',
+      source: 'api/**/*.md',
+    }),
+  },
+})