feat: live IMAP sync on folder select + 60s auto-sync interval

- New imap_sync_folder function: syncs single folder quickly for live use
- New POST /mail/folders/{folder_id}/sync route
- Frontend: syncFolder API + called on every folder selection
- Auto-sync interval reduced from 300s to 60s
- Sent mail IMAP APPEND already uploads full body via msg.as_bytes()

frontend/src/api/mail.ts

@@ -481,6 +481,10 @@ export function emptyFolder(folderId: string): Promise<{ emptied_count: number }
   return apiPost<{ emptied_count: number }>(`/mail/folders/${folderId}/empty`, {});
 }
 
+export function syncFolder(folderId: string): Promise<{ synced: number; error?: string }> {
+  return apiPost<{ synced: number; error?: string }>(`/mail/folders/${folderId}/sync`, {});
+}
+
 // ─── Mails ──────────────────────────────────────────────────────────────────
 
 export function fetchMails(folderId: string, page: number, sortBy?: string, sortOrder?: string): Promise<MailListResult> {

frontend/src/pages/Mail.tsx

@@ -35,6 +35,7 @@ import {
   saveDraft,
   updateDraft,
   triggerSync,
+  syncFolder,
   type MailAccount,
   type MailFolder,
   type Mail,
@@ -168,7 +169,7 @@ export function MailPage() {
     loadMails();
   }, [loadMails]);
 
-  // Handle folder selection — derive account from folder
+  // Handle folder selection — derive account from folder + trigger live IMAP sync
   const handleSelectFolder = useCallback(
     (folderId: string) => {
       setSelectedFolderId(folderId);
@@ -181,8 +182,13 @@ export function MailPage() {
       setSelectedMail(null);
       setSelectedMailIds(new Set());
       setActiveView('list');
+      // Live sync: fetch new mails from IMAP server immediately
+      syncFolder(folderId).then(() => {
+        loadMails();
+        loadAllFolders();
+      }).catch(() => {});
     },
-    [folders],
+    [folders, loadMails, loadAllFolders],
   );
 
   // Handle mail selection