Why is my iPhone data overriding my Apple Watch Health app data?

I have an iPhone 15 Pro Max, an Apple Watch Ultra 2, and a Garmin Fenix 7X Pro Solar. I would like the health app to collect steps only from the two watches. But this is as far as I can get.

I cannot deactivate the iPhone as a source. Which should not b e a problem, after all, if I can believe what is written below the device list: "one data source will be chosen based on the priority order listed above".

The way I use the two watches is that I use the Apple Watch for every day wear, and the Garmin for any activity (walking, running, tennis, bicycle ride, etc.).

Today I went for a walk, and was wearing the Garmin watch, while the phone was in my pocket.

When I look at the data collected, I see the iPhone was considered with higher priority than the Garmin watch, and so the iPhone data was recorded, apart from 15 steps at the beginning of the walk.

What am I doing wrong?

It is also a good question, why would the iPhone appear at all in the recorded data, since I am always wearing one watch or the other. I have a feeling even when wearing the Apple Watch, it is mostly the phone's data, that is kept.

[Re-Titled by Moderator]