### 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)

}
		}
		export_plugins.write[i]->_clear();
	}
	HashSet<String> features = get_features(p_preset, p_debug);
	PackedStringArray features_psa;
	for (const String &feature : features) {
		features_psa.push_back(feature);
	}
	
	uint32_t custom_resources_hash = HASH_MURMUR3_SEED;
	uint32_t custom_scene_hash = HASH_MURMUR3_SEED;
	LocalVector<Ref<EditorExportPlugin>> customize_resources_plugins;
	LocalVector<Ref<EditorExportPlugin>> customize_scenes_plugins;
	for (int i = 0; i < export_plugins.size(); i++) {
		if (export_plugins.write[i]->_begin_customize_resources(Ref<EditorExportPlatform>(this), features_psa)) {
			customize_resources_plugins.push_back(export_plugins[i]);
			custom_resources_hash = hash_murmur3_one_64(export_plugins[i]->get_name().hash64(), custom_resources_hash);
			uint64_t hash = export_plugins[i]->_get_customization_configuration_hash();
			custom_resources_hash = hash_murmur3_one_64(hash, custom_resources_hash);
		}
		if (export_plugins.write[i]->_begin_customize_scenes(Ref<EditorExportPlatform>(this), features_psa)) {
			customize_scenes_plugins.push_back(export_plugins[i]);
			custom_resources_hash = hash_murmur3_one_64(export_plugins[i]->get_name().hash64(), custom_resources_hash);
			uint64_t hash = export_plugins[i]->_get_customization_configuration_hash();
			custom_scene_hash = hash_murmur3_one_64(hash, custom_scene_hash);
		}
	}
	HashMap<String, FileExportCache> export_cache;
	String export_base_path = ProjectSettings::get_singleton()->get_project_data_path().path_join("exported/") + itos(custom_resources_hash);