### 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)

EditorProgress ep("savezip", TTR("Packing"), 102, true);
	Ref<FileAccess> io_fa;
	zlib_filefunc_def io = zipio_create_io(&io_fa);
	zipFile zip = zipOpen2(p_path.utf8().get_data(), APPEND_STATUS_CREATE, nullptr, &io);
	ZipData zd;
	zd.ep = &ep;
	zd.zip = zip;
	Error err = export_project_files(p_preset, p_debug, _save_zip_file, &zd);
	if (err != OK && err != ERR_SKIP) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Save ZIP"), TTR("Failed to export project files."));
	}
	zipClose(zip, nullptr);
	return OK;
}
Error EditorExportPlatform::export_pack(const Ref<EditorExportPreset> &p_preset, bool p_debug, const String &p_path, int p_flags) {