### 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)

ct = 10 + ct - 'a';
					}
					v |= ct;
				}
				key.write[i] = v;
			}
		}
	}
	Error err = OK;
	Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
	struct SortByName {
		bool operator()(const Ref<EditorExportPlugin> &left, const Ref<EditorExportPlugin> &right) const {
			return left->get_name() < right->get_name();
		}
	};
	
	export_plugins.sort_custom<SortByName>();
	for (int i = 0; i < export_plugins.size(); i++) {
		if (p_so_func) {
			for (int j = 0; j < export_plugins[i]->shared_objects.size(); j++) {
				err = p_so_func(p_udata, export_plugins[i]->shared_objects[j]);
				if (err != OK) {
					return err;
				}
			}
		}
		for (int j = 0; j < export_plugins[i]->extra_files.size(); j++) {
			err = p_func(p_udata, export_plugins[i]->extra_files[j].path, export_plugins[i]->extra_files[j].data, 0, paths.size(), enc_in_filters, enc_ex_filters, key);
			if (err != OK) {
				return err;