### 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)

save_path = export_base_path.path_join("export-" + p_path.md5_text() + "-" + base_file);
			Error err = ResourceSaver::save(res, save_path);
			ERR_FAIL_COND_V_MSG(err != OK, p_path, "Unable to save export resource file to: " + save_path);
		}
	}
	fec.saved_path = save_path;
	export_cache[p_path] = fec;
	return save_path.is_empty() ? p_path : save_path;
}
String EditorExportPlatform::_get_script_encryption_key(const Ref<EditorExportPreset> &p_preset) const {
	const String from_env = OS::get_singleton()->get_environment(ENV_SCRIPT_ENCRYPTION_KEY);
	if (!from_env.is_empty()) {
		return from_env.to_lower();
	}
	return p_preset->get_script_encryption_key().to_lower();
}
Vector<String> EditorExportPlatform::get_forced_export_files() {
	Vector<String> files;
	files.push_back(ProjectSettings::get_singleton()->get_global_class_list_path());
	String icon = GLOBAL_GET("application/config/icon");
	String splash = GLOBAL_GET("application/boot_splash/image");
	if (!icon.is_empty() && FileAccess::exists(icon)) {
		files.push_back(icon);
	}
	if (!splash.is_empty() && FileAccess::exists(splash) && icon != splash) {
		files.push_back(splash);
	}
	String resource_cache_file = ResourceUID::get_cache_file();
	if (FileAccess::exists(resource_cache_file)) {
		files.push_back(resource_cache_file);