This situation has been resolved.
Apple will introduce a redesigned Blood Oxygen feature for some Apple Watch Series 9, Series 10, and Apple Watch Ultra 2 users[…]Users[…]will have access to the redesigned Blood Oxygen feature by updating their paired iPhone to iOS 18.6.1 and their Apple Watch to watchOS 11.6.1. Following this update, sensor data from the Blood Oxygen app on Apple Watch will be measured and calculated on the paired iPhone, and results can be viewed in the Respiratory section of the Health app. This update was enabled by a recent U.S. Customs ruling.