### 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)

new_file.resize(utf8.length());
				for (int j = 0; j < utf8.length(); j++) {
					new_file.write[j] = utf8[j];
				}
				err = p_func(p_udata, from + ".remap", new_file, idx, total, enc_in_filters, enc_ex_filters, key);
				if (err != OK) {
					return err;
				}
			}
		} else {
			
			custom_map["path_remap/remapped_paths"] = path_remaps;
		}
	}
	Vector<String> forced_export = get_forced_export_files();
	for (int i = 0; i < forced_export.size(); i++) {
		Vector<uint8_t> array = FileAccess::get_file_as_bytes(forced_export[i]);
		err = p_func(p_udata, forced_export[i], array, idx, total, enc_in_filters, enc_ex_filters, key);
		if (err != OK) {
			return err;
		}
	}
	String config_file = "project.binary";
	String engine_cfb = EditorPaths::get_singleton()->get_cache_dir().path_join("tmp" + config_file);
	ProjectSettings::get_singleton()->save_custom(engine_cfb, custom_map, custom_list);
	Vector<uint8_t> data = FileAccess::get_file_as_bytes(engine_cfb);
	DirAccess::remove_file_or_error(engine_cfb);
	return p_func(p_udata, "res://" + config_file, data, idx, total, enc_in_filters, enc_ex_filters, key);
}
Error EditorExportPlatform::_add_shared_object(void *p_userdata, const SharedObject &p_so) {