I have been building and deploying to a standard Galaxy Watch, with no issues. I asked a question about Flutter on Tizen previously (Flutter on Tizen), the repository was marked as an official Samsung one.
The repository “issues” section also mentions an app being released on the Samsung Store for Galaxy Watch (Publish: Undocumented APIs is detected (allow list) · Issue #21 · flutter-tizen/flutter-tizen · GitHub).
My question was more concerned with the Flame game engine side of things.