feat: Search pagination and UX improvements

- Add pagination support to search (previously limited to 50 results)
- Search now scoped to current mailbox/folder
- Support shared mailbox folders in search
- Display total results count (e.g., "50 of 1400 conversations")
- Add clear (X) button to search input
- Re-run search when changing folders during active search
- Remove unused sidebar screenshot

app/[locale]/page.tsx

@@ -67,6 +67,8 @@ export default function Home() {
     toggleStar,
     moveToMailbox,
     searchEmails,
+    searchQuery,
+    setSearchQuery,
     isLoading,
     isLoadingEmail,
     setLoadingEmail,
@@ -469,7 +471,12 @@ export default function Home() {
     }
 
     if (client) {
-      await fetchEmails(client, mailboxId);
+      // If there's an active search, re-run it in the new mailbox
+      if (searchQuery) {
+        await searchEmails(client, searchQuery);
+      } else {
+        await fetchEmails(client, mailboxId);
+      }
     }
   };
 
@@ -483,6 +490,13 @@ export default function Home() {
     await searchEmails(client, query);
   };
 
+  const handleClearSearch = async () => {
+    setSearchQuery("");
+    if (client && selectedMailbox) {
+      await fetchEmails(client, selectedMailbox);
+    }
+  };
+
   const handleDownloadAttachment = async (blobId: string, name: string, type?: string) => {
     if (!client) return;
 
@@ -645,6 +659,8 @@ export default function Home() {
               }}
               onLogout={handleLogout}
               onSearch={handleSearch}
+              onClearSearch={handleClearSearch}
+              activeSearchQuery={searchQuery}
               quota={quota}
               isPushConnected={isPushConnected}
             />