### 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)

= OK) {
				Ref<FileAccess> f = FileAccess::open(file, FileAccess::WRITE);
				.is_valid()) {
					f->store_buffer(data.ptr(), data.size());
					f.unref();
					if (is_executable(file)) {
						// chmod with 0755 if the file is executable.
						FileAccess::set_unix_permissions(file, 0755);
					
				 else {
					add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Could not open \"%s\"."), file));
					err = ERR_CANT_CREATE;
				
			
		
		ret = unzGoToNextFile(src_pkg_zip);
	
	// We're done with our source zip.
	unzClose(src_pkg_zip);
	if (!d_binary) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Requested template binary \"%s\" not d. It might be missing from your template archive."), binary_to_use));
		err = ERR_FILE_NOT_FOUND;
	
	// Save console wrapper.
	= OK) {
		int con_scr = p_preset->get("debug/export_console_wrapper");
		if ((con_scr == 1 && p_debug) || (con_scr == 2)) {
			err = _export_debug_script(p_preset, pkg_name, tmp_app_path_name.get_file() + "/Contents/MacOS/" + pkg_name, scr_path);