### 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)

Ref<DirAccess> da = DirAccess::open(p_dest_dir);
	ERR_FAIL_COND_V_MSG(da.is_null(), ERR_CANT_OPEN, "Cannot open directory '" + p_dest_dir + "'.");
	for (uint64_t i = 0; i < sizeof(loading_screen_infos) / sizeof(loading_screen_infos[0]); ++i) {
		LoadingScreenInfo info = loading_screen_infos[i];
		String loading_screen_file = p_preset->get(info.preset_key);
		Color boot_bg_color = GLOBAL_GET("application/boot_splash/bg_color");
		String boot_logo_path = GLOBAL_GET("application/boot_splash/image");
		bool boot_logo_scale = GLOBAL_GET("application/boot_splash/fullsize");
		if (loading_screen_file.size() > 0) {
			
			Ref<Image> img = memnew(Image);
			Error err = ImageLoader::load_image(loading_screen_file, img);
			if (err != OK) {
				ERR_PRINT("Invalid loading screen (" + String(info.preset_key) + "): '" + loading_screen_file + "'.");
				return ERR_UNCONFIGURED;
			}
			if (img->get_width() != info.width || img->get_height() != info.height) {
				WARN_PRINT("Loading screen (" + String(info.preset_key) + "): '" + loading_screen_file + "' has incorrect size (" + String::num_int64(img->get_width()) + "x" + String::num_int64(img->get_height()) + ") and was automatically resized to " + String::num_int64(info.width) + "x" + String::num_int64(info.height) + ".");
				float aspect_ratio = (float)img->get_width() / (float)img->get_height();
				if (boot_logo_scale) {
					if (info.height * aspect_ratio <= info.width) {
						img->resize(info.height * aspect_ratio, info.height, (Image::Interpolation)(p_preset->get("application/launch_screens_interpolation").operator int()));
					} else {
						img->resize(info.width, info.width / aspect_ratio, (Image::Interpolation)(p_preset->get("application/launch_screens_interpolation").operator int()));
					}