feat: Online search button

- MailListView: new '🌐 Online' button in search bar
- Clicking button emits onlineSearchRequested(query)
- If search box empty, shows QInputDialog for query entry
- MainMainWindow::onOnlineSearchRequested() handler:
  - Validates current folder selected
  - Gets account for folder
  - Shows status message
  - Shows info dialog with query/folder/account (placeholder for IMAP SEARCH)
- Signal: onlineSearchRequested(const QString& query)
- Button styled in blue (online theme)

src/ui/maillistview.cpp

@@ -19,6 +19,7 @@
 #include <QMenu>
 #include <QDrag>
 #include <QMimeData>
+#include <QInputDialog>
 #include "ui/delegates/CompactMailDelegate.h"
 
 MailListView::MailListView(QWidget *parent) : QWidget(parent), m_sourceModel(nullptr), m_multiSelectMode(false)
@@ -51,6 +52,20 @@ void MailListView::setupUI()
     searchLayout->addWidget(m_searchEdit);
     connect(m_searchEdit, &QLineEdit::textChanged, this, &MailListView::onSearchTextChanged);
 
+    // Online search button
+    m_onlineSearchBtn = new QToolButton();
+    m_onlineSearchBtn->setText("🌐 Online");
+    m_onlineSearchBtn->setToolTip("Buscar en servidor (IMAP)");
+    m_onlineSearchBtn->setToolButtonStyle(Qt::ToolButtonTextBesideIcon);
+    m_onlineSearchBtn->setStyleSheet(
+        "QToolButton { background: #e3f2fd; border: 1px solid #90caf9; border-radius: 6px; "
+        "padding: 6px 12px; font-size: 12px; color: #1565c0; }"
+        "QToolButton:hover { background: #bbdefb; border-color: #42a5f5; }"
+        "QToolButton:pressed { background: #90caf9; }"
+    );
+    connect(m_onlineSearchBtn, &QToolButton::clicked, this, &MailListView::onOnlineSearchClicked);
+    searchLayout->addWidget(m_onlineSearchBtn);
+
     layout->addWidget(searchBar);
 
     // Filter bar
@@ -687,6 +702,22 @@ void MailListView::initDrag()
     Q_UNUSED(dropAction);
 }
 
+void MailListView::onOnlineSearchClicked()
+{
+    QString query = m_searchEdit->text().trimmed();
+    if (query.isEmpty()) {
+        // If search box is empty, show a dialog to enter search query
+        bool ok;
+        query = QInputDialog::getText(this, "Buscar en servidor", 
+                                      "Introduce términos de búsqueda:", 
+                                      QLineEdit::Normal, 
+                                      "", &ok);
+        if (!ok || query.trimmed().isEmpty()) return;
+    }
+    
+    emit onlineSearchRequested(query);
+}
+
 void MailListView::mousePressEvent(QMouseEvent *event)
 {
     if (event->button() == Qt::LeftButton) {

src/ui/maillistview.h

@@ -47,6 +47,8 @@ signals:
     void batchDeleteRequested(const QVector<int>& mailIds);
     void batchMarkUnreadRequested(const QVector<int>& mailIds);
     void batchMoveRequested(const QVector<int>& mailIds, int targetFolderId);
+    // Online search
+    void onlineSearchRequested(const QString& query);
 
 public slots:
     void setFolderType(const QString& folderType); // "inbox", "sent", "drafts", etc.
@@ -78,6 +80,7 @@ private slots:
     void enterMultiSelectMode();
     void exitMultiSelectMode();
     void onPivotChanged(int index);  // Focused/Other pivot
+    void onOnlineSearchClicked();
 
 protected:
     void resizeEvent(QResizeEvent *event) override;
@@ -109,6 +112,7 @@ private:
     QCheckBox *m_pinnedOnlyCheck;
     QCheckBox *m_selectAllCheck;  // Select all checkbox in action bar
     QWidget *m_actionBar;  // Action bar widget
+    QToolButton *m_onlineSearchBtn;  // Online search button
     QComboBox *m_groupByCombo;
     QComboBox *m_displayModeCombo;
     QComboBox *m_pivotCombo;  // Focused/Other pivot

src/ui/mainmainwindow.cpp

@@ -1118,3 +1118,34 @@ void MainMainWindow::onEmbeddedDetachRequested(QWidget *widget)
 
     statusBar()->showMessage(tr("Compose view detached to separate window"), 3000);
 }
+
+void MainMainWindow::onOnlineSearchRequested(const QString& query)
+{
+    if (m_currentFolderId < 0) {
+        QMessageBox::warning(this, "Buscar online", "Selecciona una carpeta primero");
+        return;
+    }
+    
+    std::optional<Folder> optFolder = FolderDao::findById(m_currentFolderId);
+    if (!optFolder.has_value()) return;
+    
+    Folder folder = optFolder.value();
+    Account* account = m_accountService->findAccountById(folder.accountId());
+    if (!account) {
+        QMessageBox::warning(this, "Buscar online", "No se encontró la cuenta para esta carpeta");
+        return;
+    }
+    
+    // Use MailService to search online (IMAP SEARCH)
+    statusBar()->showMessage(tr("Buscando en servidor: %1").arg(query), 3000);
+    
+    // TODO: Implement IMAP SEARCH in MailService
+    // For now, show a message
+    QMessageBox::information(this, "Buscar online", 
+        QString("Búsqueda en servidor para: '%1'\nCarpeta: %2\nCuenta: %3")
+            .arg(query)
+            .arg(folder.name())
+            .arg(account->email()));
+    
+    delete account;
+}

src/ui/mainmainwindow.h

@@ -82,6 +82,8 @@ private slots:
     void onReplyRequested(int mailId);
     void onForwardRequested(int mailId);
     void onMarkUnreadRequested(int mailId);
+    // Online search
+    void onOnlineSearchRequested(const QString& query);
 
     // Slots for embedded compose view
     void onEmbeddedSendRequested(const QString &to, const QString &cc, const QString &bcc,