Looks cool! Small UX note: I initially tried to enter a URL to go somewhere, but nothing happened when I pressed enter. Then I saw the "No open tabs" message, but it still took me some time to find the little button with the "+" sign.
Thanks. I don't know how to improve that right now. I'll think about it. Maybe "new tab +" ? I know the flow you refer to doesn't really work, with the omnibox there but unavailable. I don't have an idea for making it better.