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: https://git.eden-emu.dev/eden-emu/eden/pulls/125
Co-authored-by: Aleksandr Popovich <alekpopo@pm.me>
Co-committed-by: Aleksandr Popovich <alekpopo@pm.me>

src/yuzu_cmd/yuzu.cpp

@@ -1,6 +1,9 @@
 // SPDX-FileCopyrightText: 2014 Citra Emulator Project
 // SPDX-License-Identifier: GPL-2.0-or-later
 
+// SPDX-FileCopyrightText: Copyright 2025 Eden Emulator Project
+// SPDX-License-Identifier: GPL-3.0-or-later
+
 #include <chrono>
 #include <iostream>
 #include <memory>
@@ -404,7 +407,7 @@ int main(int argc, char** argv) {
     }
 
     if (use_multiplayer) {
-        if (auto member = system.GetRoomNetwork().GetRoomMember().lock()) {
+        if (auto member = Network::GetRoomMember().lock()) {
             member->BindOnChatMessageReceived(OnMessageReceived);
             member->BindOnStatusMessageReceived(OnStatusMessageReceived);
             member->BindOnStateChanged(OnStateChanged);