### 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)

if (target_sdk_str.is_valid_int()) {
			target_sdk_int = target_sdk_str.to_int();
			if (target_sdk_int > DEFAULT_TARGET_SDK_VERSION) {
				
				err += vformat(TTR("\"Target SDK\" %d is higher than the default version %d. This may work, but wasn't tested and may be unstable."), target_sdk_int, DEFAULT_TARGET_SDK_VERSION);
				err += "\n";
			}
		}
	}
	String current_renderer = GLOBAL_GET("rendering/renderer/rendering_method.mobile");
	if (current_renderer == "forward_plus") {
		
		err += vformat(TTR("The \"%s\" renderer is designed for Desktop devices, and is not suitable for Android devices."), current_renderer);
		err += "\n";
	}
	if (_uses_vulkan() && min_sdk_int < VULKAN_MIN_SDK_VERSION) {
		
		err += vformat(TTR("\"Min SDK\" should be greater or equal to %d for the \"%s\" renderer."), VULKAN_MIN_SDK_VERSION, current_renderer);
		err += "\n";
	}
	String package_name = p_preset->get("package/unique_name");
	if (package_name.find("$genname") >= 0 && !is_project_name_valid()) {
		
		err += vformat(TTR("The project name does not meet the requirement for the package name format and will be updated to \"%s\". Please explicitly specify the package name if needed."), get_valid_basename());
		err += "\n";
	}
	r_error = err;
	return valid;
}
List<String> EditorExportPlatformAndroid::get_binary_extensions(const Ref<EditorExportPreset> &p_preset) const {