docs(seo): add sitemap lastmod, local search, custom 404

Three more SEO + UX wins on top of the metadata pass:

- Sitemap now emits <lastmod> per URL (datetime, ISO-8601). Google uses
  it to prioritize recrawls — recently-edited pages get fetched faster.
- Added @easyops-cn/docusaurus-search-local: a build-time client-side
  search index with a navbar search box. No external service required;
  improves dwell-time signals and lets users land on deep pages.
- Custom /404 page with curated links to the intro, quick-start, API ref,
  recipes, and changelog (instead of Docusaurus's default generic 404).
  Reduces bounce rate when external links rot.

Author: awbx

apps/docs/docusaurus.config.js

@@ -95,6 +95,25 @@ const config = {
     },
   ],
 
+  plugins: [
+    [
+      require.resolve('@easyops-cn/docusaurus-search-local'),
+      /** @type {import('@easyops-cn/docusaurus-search-local').PluginOptions} */
+      ({
+        hashed: true,
+        indexDocs: true,
+        indexBlog: false,
+        indexPages: true,
+        docsRouteBasePath: '/docs',
+        highlightSearchTermsOnTargetPage: true,
+        searchResultLimits: 10,
+        searchBarShortcut: true,
+        searchBarShortcutHint: true,
+        explicitSearchResultPath: true,
+      }),
+    ],
+  ],
+
   presets: [
     [
       'classic',
@@ -115,6 +134,9 @@ const config = {
           priority: 0.7,
           ignorePatterns: ['/tags/**'],
           filename: 'sitemap.xml',
+          // lastmod from each doc's last update (git-tracked or frontmatter).
+          // Lets Google prioritize recrawls for recently-changed pages.
+          lastmod: 'datetime',
         },
       }),
     ],

apps/docs/package.json

@@ -23,7 +23,8 @@
   },
   "devDependencies": {
     "@docusaurus/module-type-aliases": "^3.7.0",
-    "@docusaurus/types": "^3.7.0"
+    "@docusaurus/types": "^3.7.0",
+    "@easyops-cn/docusaurus-search-local": "^0.55.1"
   },
   "browserslist": {
     "production": [

apps/docs/src/pages/404.mdx

@@ -0,0 +1,16 @@
+---
+title: Page not found
+description: That page doesn't exist (or moved). Jump to the docs intro, the quick-start, or the API reference.
+---
+
+# Page not found
+
+The URL you followed doesn't match any page on this site. A few common landings:
+
+- [**Introduction**](/docs) — what fhir-dsl is and how the pieces fit.
+- [**Quick start**](/docs/getting-started/quick-start) — install and write your first typed query.
+- [**API reference**](/docs/api/core) — every package's public surface.
+- [**Recipes**](/docs/recipes/patient-timeline) — copy-paste patterns for common tasks.
+- [**Changelog**](/docs/changelog) — what shipped recently.
+
+Try the search box at the top — it indexes every page. Or [open an issue on GitHub](https://github.com/awbx/fhir-dsl/issues) if you think a link is broken.