### 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)

destination_dir = p_out_dir.path_join(asset_path);
		asset_path = asset_path.path_join(file_name);
		destination = p_out_dir.path_join(asset_path);
	}
	Ref<DirAccess> filesystem_da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
	ERR_FAIL_COND_V_MSG(filesystem_da.is_null(), ERR_CANT_CREATE, "Cannot create DirAccess for path '" + p_out_dir + "'.");
	if (!filesystem_da->dir_exists(destination_dir)) {
		Error make_dir_err = filesystem_da->make_dir_recursive(destination_dir);
		if (make_dir_err) {
			return make_dir_err;
		}
	}
	Error err = dir_exists ? da->copy_dir(p_asset, destination) : da->copy(p_asset, destination);
	if (err) {
		return err;
	}
	if (asset_path.ends_with("/")) {
		asset_path = asset_path.left(asset_path.length() - 1);
	}
	IOSExportAsset exported_asset = { binary_name.path_join(asset_path), p_is_framework, p_should_embed };
	r_exported_assets.push_back(exported_asset);
	if (create_framework) {
		String file_name;
		if (!p_custom_file_name) {
			file_name = p_asset.get_basename().get_file();
		} else {
			file_name = *p_custom_file_name;
		}
		String framework_name = file_name + ".framework";