Add the "HA Dashboard" tab with HA's web UI (DSH-1)

A second dashboard surface shows a WebEngineView at homeassistant.url, or
a hint when none is set. HaWebUi (QML singleton owned by Dashboard) holds
the URL and a persistent WebEngine profile under
~/.local/share/frameassistant/webengine so the HA login survives restarts.
QtWebEngineQuick::initialize() runs in main() before the app object (D39).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/ha/HaWebUi.h

@@ -0,0 +1,46 @@
+#pragma once
+
+#include <QtQml/qqmlregistration.h>
+
+#include <QObject>
+#include <QQuickWebEngineProfile>
+#include <QUrl>
+
+class QJSEngine;
+class QQmlEngine;
+
+// HA's web UI in the "HA Dashboard" tab (DSH-1): the URL from the settings
+// and a persistent WebEngine profile, so the HA login survives restarts
+// (docs/DESIGN.md, D39). A QML singleton owned by the app (Dashboard).
+class HaWebUi : public QObject {
+  Q_OBJECT
+  QML_ELEMENT
+  QML_SINGLETON
+  // Empty: no URL configured (the tab shows a hint).
+  Q_PROPERTY(QUrl url READ url CONSTANT)
+  Q_PROPERTY(QQuickWebEngineProfile* profile READ profile CONSTANT)
+
+ public:
+  // Not default-constructible, so QML uses create() instead of making its
+  // own instance.
+  explicit HaWebUi(QObject* parent);
+  ~HaWebUi() override;
+
+  // Call before the QML is loaded.
+  void setUrl(const QUrl& url) { m_url = url; }
+
+  QUrl url() const { return m_url; }
+  // Created on first use: only a tab that shows the web UI needs it.
+  QQuickWebEngineProfile* profile();
+
+  // Where the profile keeps its data (cookies, local storage) and cache.
+  static QString storagePath();
+  static QString cachePath();
+
+  // QML singleton factory: the instance the app created.
+  static HaWebUi* create(QQmlEngine*, QJSEngine*);
+
+ private:
+  QUrl m_url;
+  QQuickWebEngineProfile* m_profile = nullptr;
+};