### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

const String custom_launch_image_2x = p_preset->get("storyboard/custom_image@2x");
	const String custom_launch_image_3x = p_preset->get("storyboard/custom_image@3x");
	if (custom_launch_image_2x.length() > 0 && custom_launch_image_3x.length() > 0) {
		Ref<Image> image;
		String image_path = p_dest_dir.path_join("splash@2x.png");
		image.instantiate();
		Error err = ImageLoader::load_image(custom_launch_image_2x, image);
		if (err) {
			image.unref();
			return err;
		}
		if (image->save_png(image_path) != OK) {
			return ERR_FILE_CANT_WRITE;
		}
		image.unref();
		image_path = p_dest_dir.path_join("splash@3x.png");
		image.instantiate();
		err = ImageLoader::load_image(custom_launch_image_3x, image);
		if (err) {
			image.unref();
			return err;
		}
		if (image->save_png(image_path) != OK) {
			return ERR_FILE_CANT_WRITE;