Apparently this is the key update:

> Apple’s new implementation of the blood oxygen feature on Apple Watch centers around viewing the results from a test on the iPhone rather than the watch. You start a session using the Blood Oxygen feature on your Apple Watch and the sensors on your Apple Watch will then collect the necessary data.

> The results, however, aren’t viewable on the Apple Watch itself. Instead, you can find them in the Respiratory section of the Health app on your iPhone.

I wonder if this workaround will succeed. It must be annoying for Apple to not display the results on the watch, which is obviously what users would want.