Added the public lobby to android. (#125)

This is adapted from kleidis old PR to Azahar. Changes from it:
- Fixed inconsistent button styling in the dialog for connection
- Allowed to hide both empty and full rooms.
- Proper serving of preferred games
- Enables web service for android by default
- Better implementation of multiplayer.cpp that works with oop

Also fixes the room network class and turns it into a static namespace
in network

Signed-off-by: Aleksandr Popovich <alekpopo@pm.me>

Co-authored-by: swurl <swurl@swurl.xyz>
Reviewed-on: #125
Co-authored-by: Aleksandr Popovich <alekpopo@pm.me>
Co-committed-by: Aleksandr Popovich <alekpopo@pm.me>

src/common/android/id_cache.cpp

@@ -1,7 +1,7 @@
 // SPDX-FileCopyrightText: Copyright 2023 yuzu Emulator Project
 // SPDX-License-Identifier: GPL-2.0-or-later
 
-// SPDX-FileCopyrightText: Copyright yuzu/Citra Emulator Project / Eden Emulator Project
+// SPDX-FileCopyrightText: 2025 Eden Emulator Project
 // SPDX-License-Identifier: GPL-3.0-or-later
 
 #include <jni.h>
@@ -94,10 +94,10 @@ static jmethodID s_yuzu_input_device_get_supports_vibration;
 static jmethodID s_yuzu_input_device_vibrate;
 static jmethodID s_yuzu_input_device_get_axes;
 static jmethodID s_yuzu_input_device_has_keys;
+
 static jmethodID s_add_netplay_message;
 static jmethodID s_clear_chat;
 
-
 static constexpr jint JNI_VERSION = JNI_VERSION_1_6;
 
 namespace Common::Android {
@@ -405,7 +405,6 @@ jmethodID ClearChat() {
     return s_clear_chat;
 }
 
-
 #ifdef __cplusplus
 extern "C" {
 #endif
@@ -605,7 +604,7 @@ void JNI_OnUnload(JavaVM* vm, void* reserved) {
     // UnInitialize applets
     SoftwareKeyboard::CleanupJNI(env);
 
-    NetworkShutdown();
+    AndroidMultiplayer::NetworkShutdown();
 }
 
 #ifdef __cplusplus