docs(website): move the API version selector into the header (prominent, /api-only)

The version selector now renders in the top bar on /api/** pages instead of only in the sidebar (where it was easy to miss, and never seen until you were deep inside a versioned page). Reuses the existing VersionSwitcher (which self-hides off /api/**), restyled compact for the header; removed the duplicate sidebar mount. Verified: the version select renders on /api/<version>/** pages and is absent on the landing, guides, and the /api overview.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: Roger-luo

website/src/components/Sidebar.astro

@@ -9,8 +9,8 @@
  * every other page shows the stock sidebar unchanged.
  */
 import Default from '@astrojs/starlight/components/Sidebar.astro';
-import VersionSwitcher from './VersionSwitcher.astro';
 ---
 
-<VersionSwitcher />
+{/* The API version selector now lives in the site header (SiteHeader.astro);
+    this override is a pass-through kept for future sidebar customization. */}
 <Default><slot /></Default>

website/src/components/SiteHeader.astro

@@ -19,6 +19,9 @@
 import { primaryNav, githubUrl } from '../lib/nav';
 import logoLight from '../assets/logo.svg';
 import logoDark from '../assets/logo-dark.svg';
+// API version selector — self-hides unless the current URL is /api/<version>/…,
+// so it only appears in the header on versioned API pages.
+import VersionSwitcher from './VersionSwitcher.astro';
 
 interface Props {
   /** Render the (docs-only) search slot region. */
@@ -41,6 +44,8 @@ const { withSearch = false } = Astro.props;
     )
   }
 
+  <VersionSwitcher />
+
   <nav class="site-nav" aria-label="Primary">
     {
       primaryNav.map((item) => (

website/src/components/VersionSwitcher.astro

@@ -75,13 +75,12 @@ const show = current !== null && manifest.versions.length > 0;
 </script>
 
 <style>
+  /* Compact, inline treatment for the site header (the switcher now lives in
+     the top bar rather than the sidebar). */
   .version-switcher {
     display: flex;
     align-items: center;
-    gap: 0.5rem;
-    padding: 0.5rem 0 0.75rem;
-    margin-bottom: 0.5rem;
-    border-bottom: 1px solid var(--sl-color-hairline-light);
+    gap: 0.4rem;
   }
   .version-switcher__label {
     font-size: var(--sl-text-xs);
@@ -91,9 +90,9 @@ const show = current !== null && manifest.versions.length > 0;
     color: var(--sl-color-gray-3);
   }
   .version-switcher__select {
-    flex: 1 1 auto;
+    flex: 0 0 auto;
     min-width: 0;
-    padding: 0.3rem 0.5rem;
+    padding: 0.25rem 0.5rem;
     font-size: var(--sl-text-sm);
     color: var(--sl-color-white);
     background-color: var(--sl-color-black);