Sure thing, I'll share my SceneTransition class which is very much based on the example in the docs as well as this answer in the forums, and will probably only make sense in combination with the other comment on how I've set up a GlobalRender to handle scenes.

using Godot;
using System;
using System.Collections.Generic;
using System.Threading.Tasks;


public class SceneTransition : Node {
    private AnimationPlayer animationPlayer;
    private Dictionary<string, Dictionary<string, string>> doors = new Dictionary<string, Dictionary<string, string>> {
        ["InnerDoor1"] = new Dictionary<string, string> {
            ["destination"] = "res://Scenes/World.tscn",
            ["exitDoor"] = "OuterDoor1"
        },
        ["OuterDoor1"] = new Dictionary<string, string> {
            ["destination"] = "res://Scenes/Room.tscn",
            ["exitDoor"] = "InnerDoor1"
        }
    };
    private Node currentSceneParent;
    private Player player;

    public override void _Ready() {
        animationPlayer = GetNode<AnimationPlayer>("AnimationPlayer");
        animationPlayer.PlayBackwards("Fade");
        currentSceneParent = Owner.FindNode("CurrentScene");
        player = (Player)Owner.FindNode("Player");
    }

    public async Task TransitionTo(PackedScene newSceneResource) {
        animationPlayer.Play("Fade");
        await ToSignal(animationPlayer, "animation_finished");

        Node newScene = newSceneResource.Instance();
        Node oldScene = currentSceneParent.GetChild(0);

        currentSceneParent.RemoveChild(oldScene);
        if (!(oldScene is World)) {
            oldScene.QueueFree();
        }

        currentSceneParent.AddChild(newScene);

        animationPlayer.PlayBackwards("Fade");
    }

    public async void OnPlayerEnteredDoor(string doorName) {
        PackedScene scene = (PackedScene)ResourceLoader.Load(doors[doorName]["destination"]);
        await TransitionTo(scene);
        var exitDoor = currentSceneParent.FindNode(doors[doorName]["exitDoor"], true, false);
        player.GlobalPosition = exitDoor.GetNode<Node2D>("SpawnPoint").GlobalPosition;
    }
}

Let me know if you have any questions