### 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)

while (!path.is_empty()) {
		if (p_da->current_is_dir()) {
			if (path != "." && path != "..") {
				dirs.push_back(path);
			}
		} else {
			Error err = p_handler(current_dir.path_join(path), p_userdata);
			if (err) {
				p_da->list_dir_end();
				return err;
			}
		}
		path = p_da->get_next();
	}
	p_da->list_dir_end();
	for (int i = 0; i < dirs.size(); ++i) {
		String dir = dirs[i];
		p_da->change_dir(dir);
		Error err = _walk_dir_recursive(p_da, p_handler, p_userdata);
		p_da->change_dir("..");
		if (err) {
			return err;
		}
	}
	return OK;
}
struct CodesignData {
	const Ref<EditorExportPreset> &preset;
	bool debug = false;
	CodesignData(const Ref<EditorExportPreset> &p_preset, bool p_debug) :