### 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)

if (!apk_expansion) {
			print_verbose("Exporting project files...");
			CustomExportData user_data;
			user_data.assets_directory = assets_directory;
			user_data.debug = p_debug;
			if (p_flags & DEBUG_FLAG_DUMB_CLIENT) {
				err = export_project_files(p_preset, p_debug, ignore_apk_file, &user_data, copy_gradle_so);
			} else {
				err = export_project_files(p_preset, p_debug, rename_and_store_file_in_gradle_project, &user_data, copy_gradle_so);
			}
			if (err != OK) {
				add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), TTR("Could not export project files to gradle project."));
				return err;
			}
			if (user_data.libs.size() > 0) {
				Ref<FileAccess> fa = FileAccess::open(GDEXTENSION_LIBS_PATH, FileAccess::WRITE);
				fa->store_string(JSON::stringify(user_data.libs, "\t"));
			}
		} else {
			print_verbose("Saving apk expansion file...");
			err = save_apk_expansion_file(p_preset, p_debug, p_path);
			if (err != OK) {
				add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), TTR("Could not write expansion package file!"));
				return err;
			}
		}
		print_verbose("Storing command line flags...");
		store_file_at_path(assets_directory + "/_cl_", command_line_flags);
		print_verbose("Updating ANDROID_HOME environment to " + sdk_path);
		OS::get_singleton()->set_environment("ANDROID_HOME", sdk_path);