As per How does it work? section in the main readme, this extension reads some data that you enter directly (e.g. workout count) as well as data from your Garmin Connect profile page.
The only network calls this extension makes are to the relevant Garmin Connect backend services in order to download workouts; other than that all data you enter or receive never leaves your device.
If you download the extension via your browser's official extension store, your browser may collect basic information about you such as geographic region, age bracket, gender etc, and use it for analytics purposes (e.g. the Chrome Web Store seems to be pretty tightly integrated with Google Analytics). Some of this information may be shared with the maintainers of Garmin Workout Downloader which we may use for various purposes such as informing development decisions. We expect all data we receive at this stage to be aggregated and anonymized.
If you choose to submit a GitHub issue on this project or contribute via a Pull Request, GitHub will collect and publish some information such as your username. Refer to GitHub's Privacy Policy for more information.