Autoload.cs

using Godot;

namespace Gamma.Core
{
    public class Autoload : Node
    {
        private Node _scene;

        public override void _Ready()
        {
            _scene = Game.CurrentScene();
        }
        
        public override void _Notification(int what)
        {
            if (what == MainLoop.NotificationWmQuitRequest)
                Quit();
        }

        public void Quit()
        {
            GetTree().Quit(); // default behavior
        }

        public void SwitchScene(string path)
        {
            CallDeferred(nameof(SwitchSceneCallback), path);
        }

        public void SwitchSceneCallback(string path)
        {
            _scene.Free();
            _scene = GD.Load<PackedScene>(path).Instance();
            Game.Root().AddChild(_scene);
            GetTree().SetCurrentScene(_scene);
        }
    }
}

Game.cs

using Godot;

namespace Gamma.Core
{
    public class Game
    {
        public static Game Instance => _instance ?? (_instance = new Game());
        private static Game _instance;

        private bool _initiated;
        private Viewport _root;

        private Game()
        {
            Init();
        }

        public void Init()
        {
            if(_initiated) return;

            _initiated = true;
            _root = ((SceneTree) Engine.GetMainLoop()).GetRoot();
        }

        public static Viewport Root()
        {
            return Instance._root;
        }

        public static Node CurrentScene()
        {
            var root = Root();
            return root?.GetChild(root.GetChildCount() - 1);
        }

        public static Autoload Autoload()
        {
            return Root().GetNode<Autoload>("Autoload");
        }

        public static void ExitGame()
        {
            Autoload().Quit();
        }
    }
}

SceneSwitcher.cs

using System;
using System.Collections.Generic;
using Gamma.Core.Scripts;

namespace Gamma.Core
{
    public enum Scenes
    {
        MainMenu,
        Options,
        Credits,
    }
    public class SceneSwitcher
    {
        private static readonly Dictionary<Scenes, string> ScenesDict = new Dictionary<Scenes, string>
        {
            {Scenes.MainMenu, "MainMenu"},
            {Scenes.Options, ""},
            {Scenes.Credits, "Credits"},
        };

        public static void Switch(Scenes scene)
        {
            if(!ScenesDict.ContainsKey(scene))
            {
                throw new Exception($"Invalid scene you are trying to switch to: {scene}");
            }
            
            Game.Autoload().SwitchScene($"res://Data/Scenes/{ScenesDict[scene]}.tscn");
        }
    }
}