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/core/core.h

@@ -1,6 +1,9 @@
 // SPDX-FileCopyrightText: 2014 Citra Emulator Project
 // SPDX-License-Identifier: GPL-2.0-or-later
 
+// SPDX-FileCopyrightText: 2025 Eden Emulator Project
+// SPDX-License-Identifier: GPL-3.0-or-later
+
 #pragma once
 
 #include <cstddef>
@@ -104,10 +107,6 @@ namespace Core::HID {
 class HIDCore;
 }
 
-namespace Network {
-class RoomNetwork;
-}
-
 namespace Tools {
 class RenderdocAPI;
 }
@@ -380,12 +379,6 @@ public:
     [[nodiscard]] Core::Debugger& GetDebugger();
     [[nodiscard]] const Core::Debugger& GetDebugger() const;
 
-    /// Gets a mutable reference to the Room Network.
-    [[nodiscard]] Network::RoomNetwork& GetRoomNetwork();
-
-    /// Gets an immutable reference to the Room Network.
-    [[nodiscard]] const Network::RoomNetwork& GetRoomNetwork() const;
-
     [[nodiscard]] Tools::RenderdocAPI& GetRenderdocAPI();
 
     void SetExitLocked(bool locked);