It does not except in a single case. All the data is stored locally in the browser extension storage otherwise. As part of the onboarding flow you can choose to anonymously submit your money saved to the online tally at https://www.curbyourconsumerism.app/
I realize there have been browser extension authenticity issues recently with some sketchy things being published like The Great Suspender https://github.com/greatsuspender/thegreatsuspender/issues/1.... I've got to spend more time investigating a way to remove this question for users, but my intent is to never collect any data beyond the anonymous online tally of the homepage which is opt-in only.
Sorry, I need to replace that email address it is unfortunately a placeholder. Side project has some loose threads. I'll do that tonight.
I couldn't find stated clearly one way or the other whether or not you collect information about the sites that I visit.