### 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)

case PluginConfigIOS::PlistItemType::STRING_INPUT: {
					String preset_name = "plugins_plist/" + key;
					String input_value = p_preset->get(preset_name);
					value = "<string>" + input_value + "</string>";
				} break;
				default:
					value = item.value;
					break;
			}
			if (key.is_empty() || value.is_empty()) {
				continue;
			}
			String plist_key = "<key>" + key + "</key>";
			plist_values[plist_key] = value;
		}
		
		String definition_comment = "// Plugin: " + plugin.name + "\n";
		String initialization_method = plugin.initialization_method + "();\n";
		String deinitialization_method = plugin.deinitialization_method + "();\n";
		plugin_definition_cpp_code += definition_comment +
				"extern void " + initialization_method +
				"extern void " + deinitialization_method + "\n";
		plugin_initialization_cpp_code += "\t" + initialization_method;
		plugin_deinitialization_cpp_code += "\t" + deinitialization_method;
		if (plugin.use_swift_runtime) {
			p_config_data.use_swift_runtime = true;
		}
	}
	
	{