feat: Add lobby API URL configuration and migrate from web_api_url

- Replace web_api_url references with lobby_api_url
- Add lobby API URL field to network configuration UI with restore default
- Add ReadNetworkValues/SaveNetworkValues to QtConfig for network settings
- Fix signed/unsigned comparison in lobby filter

Signed-off-by: Zephyron <zephyron@citron-emu.org>

src/citron/configuration/configure_network.h

@@ -1,15 +1,22 @@
 // SPDX-FileCopyrightText: Copyright 2019 yuzu Emulator Project
+// SPDX-FileCopyrightText: 2025 citron Emulator Project
 // SPDX-License-Identifier: GPL-2.0-or-later
 
 #pragma once
 
 #include <memory>
+#include <string> // Required for std::string
 #include <QWidget>
 
 namespace Ui {
 class ConfigureNetwork;
 }
 
+// Forward declare Core::System
+namespace Core {
+class System;
+}
+
 class ConfigureNetwork : public QWidget {
     Q_OBJECT
 
@@ -19,12 +26,17 @@ public:
 
     void ApplyConfiguration();
 
+private slots:
+    void OnRestoreDefaultLobbyApi();
+
 private:
     void changeEvent(QEvent*) override;
     void RetranslateUI();
     void SetConfiguration();
 
     std::unique_ptr<Ui::ConfigureNetwork> ui;
-
     const Core::System& system;
+
+    // This stores the URL
+    std::string original_lobby_api_url;
 };