refactor: Restructure monorepo to apps/server/ and apps/web/ layout

Move src/ → apps/server/ and packages/web/ → apps/web/ to adopt
standard monorepo conventions (apps/ for runnable apps, packages/
for reusable libraries). Update all config files, shared package
imports, test fixtures, and documentation to reflect new paths.

Key fixes:
- Update workspace config to ["apps/*", "packages/*"]
- Update tsconfig.json rootDir/include for apps/server/
- Add apps/web/** to vitest exclude list
- Update drizzle.config.ts schema path
- Fix ensure-schema.ts migration path detection (3 levels up in dev,
  2 levels up in dist)
- Fix tests/integration/cli-server.test.ts import paths
- Update packages/shared imports to apps/server/ paths
- Update all docs/ files with new paths

apps/server/agent/markdown-to-tiptap.ts

@@ -0,0 +1,32 @@
+/**
+ * Server-side Markdown → Tiptap JSON converter.
+ *
+ * Uses @tiptap/markdown's MarkdownManager.parse() — the same approach
+ * as content-serializer.ts but in reverse direction.
+ * No DOM needed, no new dependencies.
+ */
+
+import StarterKit from '@tiptap/starter-kit';
+import Link from '@tiptap/extension-link';
+import { MarkdownManager } from '@tiptap/markdown';
+
+let _manager: MarkdownManager | null = null;
+
+function getManager(): MarkdownManager {
+  if (!_manager) {
+    _manager = new MarkdownManager({
+      extensions: [StarterKit, Link],
+    });
+  }
+  return _manager;
+}
+
+/**
+ * Convert a markdown string to Tiptap JSON document.
+ */
+export function markdownToTiptapJson(markdown: string): object {
+  if (!markdown.trim()) {
+    return { type: 'doc', content: [{ type: 'paragraph' }] };
+  }
+  return getManager().parse(markdown);
+}