### 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<EditorExportPreset> current = get_current_preset();
	ERR_FAIL_COND(current.is_null());
	Ref<EditorExportPlatform> platform = current->get_platform();
	ERR_FAIL_COND(platform.is_null());
	export_project->set_access(EditorFileDialog::ACCESS_FILESYSTEM);
	export_project->clear_filters();
	List<String> extension_list = platform->get_binary_extensions(current);
	for (int i = 0; i < extension_list.size(); i++) {
		
		export_project->add_filter("*." + extension_list[i], vformat(TTR("%s Export"), platform->get_name()));
	}
	if (!current->get_export_path().is_empty()) {
		export_project->set_current_path(current->get_export_path());
	} else {
		if (extension_list.size() >= 1) {
			export_project->set_current_file(default_filename + "." + extension_list[0]);
		} else {
			export_project->set_current_file(default_filename);
		}
	}
	
	
	
	
	if (!export_project->get_line_edit()->is_connected("text_submitted", callable_mp(export_project, &EditorFileDialog::_file_submitted))) {
		export_project->get_ok_button()->set_disabled(false);
		export_project->get_line_edit()->connect("text_submitted", callable_mp(export_project, &EditorFileDialog::_file_submitted));
	}