### 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)

return ERR_CANT_CREATE;
		} else {
			print_verbose(copy_binary_output);
		}
		print_verbose("Successfully completed Android gradle build.");
		return OK;
	}
	
	print_verbose("Starting legacy build system...");
	if (p_debug) {
		src_apk = p_preset->get("custom_template/debug");
	} else {
		src_apk = p_preset->get("custom_template/release");
	}
	src_apk = src_apk.strip_edges();
	if (src_apk.is_empty()) {
		if (p_debug) {
			src_apk = find_export_template("android_debug.apk");
		} else {
			src_apk = find_export_template("android_release.apk");
		}
		if (src_apk.is_empty()) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Package not found: \"%s\"."), src_apk));
			return ERR_FILE_NOT_FOUND;
		}
	}
	if (!DirAccess::exists(p_path.get_base_dir())) {
		return ERR_FILE_BAD_PATH;
	}
	Ref<FileAccess> io_fa;