### 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 (p_node != nullptr && p_node != p_root) {
		if (p_root->is_editable_instance(p_node)) {
			return true;
		}
		p_node = p_node->get_owner();
	}
	return false;
}
bool EditorExportPlatform::_export_customize_scene_resources(Node *p_root, Node *p_node, LocalVector<Ref<EditorExportPlugin>> &customize_resources_plugins) {
	bool changed = false;
	if (p_root == p_node || p_node->get_owner() == p_root || _is_editable_ancestor(p_root, p_node)) {
		if (_export_customize_object(p_node, customize_resources_plugins)) {
			changed = true;
		}
	}
	for (int i = 0; i < p_node->get_child_count(); i++) {
		if (_export_customize_scene_resources(p_root, p_node->get_child(i), customize_resources_plugins)) {
			changed = true;
		}
	}
	return changed;
}
String EditorExportPlatform::_export_customize(const String &p_path, LocalVector<Ref<EditorExportPlugin>> &customize_resources_plugins, LocalVector<Ref<EditorExportPlugin>> &customize_scenes_plugins, HashMap<String, FileExportCache> &export_cache, const String &export_base_path, bool p_force_save) {