Just to follow up on this, excluding .small means you will not customize the live activity on the smart stack on the watch, but it does still show up.
We have a similar issue, where we have an iOS app with a watch companion. The challenge we have is during a workout (we're a workout app), we display a live activity on the phone, which syncs to the watch.
The watch smart stack then shows TWO widgets:
The native workout widget
The mirrored live activity from the phone
This feels a bit redundant and unnecessary, but from what I'm reading there is no way to disable mirroring of the live activity all together, only disable customization.