### 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)

if (p->get_platform() == preset->get_platform() && p->is_runnable()) {
				make_runnable = false;
			}
			if (p->get_name() == preset_name) {
				valid = false;
				break;
			}
		}
		if (valid) {
			break;
		}
		preset_name += " (copy)";
	}
	preset->set_name(preset_name);
	if (make_runnable) {
		preset->set_runnable(make_runnable);
	}
	preset->set_dedicated_server(current->is_dedicated_server());
	preset->set_export_filter(current->get_export_filter());
	preset->set_include_filter(current->get_include_filter());
	preset->set_exclude_filter(current->get_exclude_filter());
	preset->set_custom_features(current->get_custom_features());
	for (const KeyValue<StringName, Variant> &E : current->get_values()) {
		preset->set(E.key, E.value);
	}
	EditorExport::get_singleton()->add_export_preset(preset);
	_update_presets();
	_edit_preset(EditorExport::get_singleton()->get_export_preset_count() - 1);
}
void ProjectExportDialog::_delete_preset() {