### 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)

bool scale_splash = GLOBAL_GET("application/boot_splash/fullsize");
	bool apply_filter = GLOBAL_GET("application/boot_splash/use_filter");
	bool show_splash_image = GLOBAL_GET("application/boot_splash/show_image");
	String project_splash_path = GLOBAL_GET("application/boot_splash/image");
	
	bool bg_color_valid = false;
	Color bg_color = ProjectSettings::get_singleton()->get("application/boot_splash/bg_color", &bg_color_valid);
	if (!bg_color_valid) {
		bg_color = boot_splash_bg_color;
	}
	if (show_splash_image) {
		if (!project_splash_path.is_empty()) {
			splash_image.instantiate();
			print_verbose("Loading splash image: " + project_splash_path);
			const Error err = ImageLoader::load_image(project_splash_path, splash_image);
			if (err) {
				if (OS::get_singleton()->is_stdout_verbose()) {
					print_error("- unable to load splash image from " + project_splash_path + " (" + itos(err) + ")");
				}
				splash_image.unref();
			}
		}
	} else {
		splash_image.instantiate();