### 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)

zlib_filefunc_def io = zipio_create_io(&io_fa);
	if (ep.step(TTR("Creating APK..."), 0)) {
		return ERR_SKIP;
	}
	unzFile pkg = unzOpen2(src_apk.utf8().get_data(), &io);
	if (!pkg) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Could not find template APK to export: \"%s\"."), src_apk));
		return ERR_FILE_NOT_FOUND;
	}
	int ret = unzGoToFirstFile(pkg);
	Ref<FileAccess> io2_fa;
	zlib_filefunc_def io2 = zipio_create_io(&io2_fa);
	String tmp_unaligned_path = EditorPaths::get_singleton()->get_cache_dir().path_join("tmpexport-unaligned." + uitos(OS::get_singleton()->get_unix_time()) + ".apk");
#define CLEANUP_AND_RETURN(m_err)                            \
	{                                                        \
		DirAccess::remove_file_or_error(tmp_unaligned_path); \
		return m_err;                                        \
	}                                                        \
	((void)0)
	zipFile unaligned_apk = zipOpen2(tmp_unaligned_path.utf8().get_data(), APPEND_STATUS_CREATE, nullptr, &io2);
	String cmdline = p_preset->get("command_line/extra_args");
	String version_name = p_preset->get_version("version/name");
	String package_name = p_preset->get("package/unique_name");
	String apk_expansion_pkey = p_preset->get("apk_expansion/public_key");
	Vector<ABI> invalid_abis(enabled_abis);
	while (ret == UNZ_OK) {
		
		unz_file_info info;
		char fname[16384];
		ret = unzGetCurrentFileInfo(pkg, &info, fname, 16384, nullptr, 0, nullptr, 0);