feat: add Microsoft Clarity analytics provider

Add Microsoft Clarity as a fourth analytics provider option alongside
Umami, Google Analytics, and Custom. Clarity provides free heatmaps,
session recordings, and user analytics.

- admin.types.ts: Add 'clarity' to AnalyticsProvider union type
- api/admin/site/route.ts: Add 'clarity' to validation
- admin/page.tsx: Add Clarity option to dropdown + Project ID input UI
- layout.tsx: Inject Clarity tracking script with project ID

src/app/layout.tsx

@@ -116,7 +116,7 @@ export default async function RootLayout({
   let webLiveEnabled = false;
   let customAdFilterVersion = 0;
   let analyticsEnabled = false;
-  let analyticsProvider: 'umami' | 'google' | 'custom' = 'umami';
+  let analyticsProvider: 'umami' | 'google' | 'clarity' | 'custom' = 'umami';
   let analyticsScriptUrl = '';
   let analyticsWebsiteId = '';
   let analyticsCustomScript = '';
@@ -372,6 +372,13 @@ export default async function RootLayout({
             />
           </>
         )}
+        {analyticsEnabled && analyticsProvider === 'clarity' && analyticsWebsiteId && (
+          <script
+            dangerouslySetInnerHTML={{
+              __html: `(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)};t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window,document,"clarity","script","${analyticsWebsiteId}");`,
+            }}
+          />
+        )}
         {analyticsEnabled && analyticsProvider === 'custom' && analyticsCustomScript && (
           <script
             dangerouslySetInnerHTML={{ __html: analyticsCustomScript }}