### 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<FileAccess> f = FileAccess::open(sw_path, FileAccess::READ);
		if (f.is_null()) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("PWA"), vformat(TTR("Could not read file: \"%s\"."), sw_path));
			return ERR_FILE_CANT_READ;
		}
		sw.resize(f->get_length());
		f->get_buffer(sw.ptrw(), sw.size());
	}
	_replace_strings(replaces, sw);
	Error err = _write_or_error(sw.ptr(), sw.size(), dir.path_join(name + ".service.worker.js"));
	if (err != OK) {
		return err;
	}
	
	const String offline_page = p_preset->get("progressive_web_app/offline_page");
	if (!offline_page.is_empty()) {
		Ref<DirAccess> da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
		const String offline_dest = dir.path_join(name + ".offline.html");
		err = da->copy(ProjectSettings::get_singleton()->globalize_path(offline_page), offline_dest);
		if (err != OK) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("PWA"), vformat(TTR("Could not read file: \"%s\"."), offline_dest));
			return err;
		}
	}
	
	const char *modes[4] = { "fullscreen", "standalone", "minimal-ui", "browser" };
	const char *orientations[3] = { "any", "landscape", "portrait" };
	const int display = CLAMP(int(p_preset->get("progressive_web_app/display")), 0, 4);
	const int orientation = CLAMP(int(p_preset->get("progressive_web_app/orientation")), 0, 3);
	Dictionary manifest;