How to update Tumbleweed

I know that the proper way to update Tumbleweed is with “zypper dup” but I have seen some remarks here suggesting that the Software Update app has been modified for Tumbleweed to do a “zypper dup”. I have not seen anything definitive, though.

So, is it OK now to use the Software Update app to update Tumbleweed?

If you mean the applets for GNOME and KDE, yes. They perform a dup on TW since a while.