### 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)

Ref<EditorExportPlatform> platform = p_preset->get_platform();
	List<String> feature_list;
	platform->get_platform_features(&feature_list);
	platform->get_preset_features(p_preset, &feature_list);
	HashSet<String> result;
	for (const String &E : feature_list) {
		result.insert(E);
	}
	result.insert("template");
	if (p_debug) {
		result.insert("debug");
		result.insert("template_debug");
	} else {
		result.insert("release");
		result.insert("template_release");
	}
	if (!p_preset->get_custom_features().is_empty()) {
		Vector<String> tmp_custom_list = p_preset->get_custom_features().split(",");
		for (int i = 0; i < tmp_custom_list.size(); i++) {
			String f = tmp_custom_list[i].strip_edges();
			if (!f.is_empty()) {
				result.insert(f);
			}
		}
	}
	return result;
}
EditorExportPlatform::ExportNotifier::ExportNotifier(EditorExportPlatform &p_platform, const Ref<EditorExportPreset> &p_preset, bool p_debug, const String &p_path, int p_flags) {