### 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)

PluginConfigIOS plugin = enabled_plugins[i];
		
		String plugin_main_binary = PluginConfigIOS::get_plugin_main_binary(plugin, p_debug);
		String plugin_binary_result_file = plugin.binary.get_file();
		
		
		err = _copy_asset(dest_dir, plugin_main_binary, &plugin_binary_result_file, true, false, r_exported_assets);
		ERR_FAIL_COND_V(err, err);
		
		
		for (int j = 0; j < plugin.linked_dependencies.size(); j++) {
			String dependency = plugin.linked_dependencies[j];
			String name = dependency.get_file();
			if (added_linked_dependenciy_names.has(name)) {
				continue;
			}
			added_linked_dependenciy_names.push_back(name);
			plugin_linked_dependencies.push_back(dependency);
		}
		for (int j = 0; j < plugin.system_dependencies.size(); j++) {
			String dependency = plugin.system_dependencies[j];
			String name = dependency.get_file();
			if (added_linked_dependenciy_names.has(name)) {
				continue;
			}
			added_linked_dependenciy_names.push_back(name);
			plugin_linked_dependencies.push_back(dependency);
		}
		for (int j = 0; j < plugin.embedded_dependencies.size(); j++) {
			String dependency = plugin.embedded_dependencies[j];