### 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)

bool force_binary = convert_text_to_binary && (path.get_extension().to_lower() == "tres" || path.get_extension().to_lower() == "tscn");
				String export_path = _export_customize(path, customize_resources_plugins, customize_scenes_plugins, export_cache, export_base_path, force_binary);
				if (export_path != path) {
					
					path_remaps.push_back(path);
					path_remaps.push_back(export_path);
				}
				Vector<uint8_t> array = FileAccess::get_file_as_bytes(export_path);
				err = p_func(p_udata, export_path, array, idx, total, enc_in_filters, enc_ex_filters, key);
				if (err != OK) {
					return err;
				}
			}
		}
		idx++;
	}
	if (convert_text_to_binary || !customize_resources_plugins.is_empty() || !customize_scenes_plugins.is_empty()) {
		
		String fcache = export_base_path.path_join("file_cache");
		Ref<FileAccess> f = FileAccess::open(fcache, FileAccess::WRITE);
		if (f.is_valid()) {
			for (const KeyValue<String, FileExportCache> &E : export_cache) {
				if (E.value.used) { 
					String l = E.key + "::" + E.value.source_md5 + "::" + itos(E.value.source_modified_time) + "::" + E.value.saved_path;
					f->store_line(l);
				}
			}
		} else {
			ERR_PRINT("Error opening export file cache: " + fcache);
		}