Tried this with a throwaway, but it's broken.
Subscription location has changed.
When corrected, it asks to visit https://cors-anywhere.herokuapp.com/corsdemo to request access. Despite doing so, it never gets past that point.
When/if you fix it, you might give some context about how you're handling user credentials.
A Google image search of the icon wasn't super helpful, but did return a similar-looking image named "style" among the results.
Knowing that Liftoff is written in Flutter, I confirmed that it is called the "style" icon.
A search of the Liftoff code on GitHub for the "style" icon turned up a match with the comment:
So the answer is that it does nothing now, but appears like it might be used in the future to "change styles." Maybe as a shortcut to the "Post Style" screen in "Settings."