### 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)

DirAccess::remove_file_or_error(tmp_export_path); \
		return m_err;                                     \
	}                                                     \
	((void)0)
	
	Error err = export_project_helper(p_preset, true, tmp_export_path, EXPORT_FORMAT_APK, true, p_debug_flags);
	if (err != OK) {
		CLEANUP_AND_RETURN(err);
	}
	List<String> args;
	int rv;
	String output;
	bool remove_prev = EDITOR_GET("export/android/one_click_deploy_clear_previous_install");
	String version_name = p_preset->get_version("version/name");
	String package_name = p_preset->get("package/unique_name");
	if (remove_prev) {
		if (ep.step(TTR("Uninstalling..."), 1)) {
			CLEANUP_AND_RETURN(ERR_SKIP);
		}
		print_line("Uninstalling previous version: " + devices[p_device].name);
		args.push_back("-s");
		args.push_back(devices[p_device].id);
		args.push_back("uninstall");
		args.push_back(get_package_name(package_name));
		output.clear();
		err = OS::get_singleton()->execute(adb, args, &output, &rv, true);
		print_verbose(output);
	}
	print_line("Installing to device (please wait...): " + devices[p_device].name);
	if (ep.step(TTR("Installing to device, please wait..."), 2)) {