### 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)

// Create a Installer.
			= OK) {
				if (ep.step(TTR("Making PKG installer"), 3)) {
					return ERR_SKIP;
				
				err = _create_pkg(p_preset, p_path, tmp_app_path_name);
			
		 else if (export_format == "zip") {
			// Create ZIP.
			= OK) {
				if (ep.step(TTR("Making ZIP"), 3)) {
					return ERR_SKIP;
				
				if (FileAccess::exists(p_path)) {
					OS::get_singleton()->move_to_trash(p_path);
				
				Ref<FileAccess> io_fa_dst;
				zlib_filefunc_def io_dst = zipio_create_io(&io_fa_dst);
				zipFile zip = zipOpen2(p_path.utf8().get_data(), APPEND_STATUS_CREATE, nullptr, &io_dst);
				zip_folder_recursive(zip, tmp_base_path_name, "", pkg_name);
				zipClose(zip, nullptr);
			
		
		bool noto_enabled = (p_preset->get("notarization/notarization").operator int() > 0);
		= OK && noto_enabled) {
			if (export_format == "app" || export_format == "pkg") {
				add_message(EXPORT_MESSAGE_INFO, TTR("Notarization"), TTR("Notarization requires the app to be archived first, select the DMG or ZIP export format instead."));
			 else {
				if (ep.step(TTR("Sending archive for notarization"), 4)) {
					return ERR_SKIP;