Teksti does not store personally identifiable information on its users or visitors. If you choose a recognizable user name or email for you account then it's on you.
Web fiction reading selections of Teksti's users are private by default. They are used in aggregate form for recommendations and other site features.
Teksti does not use tracking cookies. Cookies are used for site features like sessions for logged in users. Just visiting the site without logging in sets no cookies.
Teksti allows connecting accounts using OAuth2 with a number of service providers. If you do so, Teksti will store the minimum amount of user data on its end.
Teksti does not share users' emails or other preferences with anyone, if it can avoid it. I'm not sure what legal action could make it necessary. I can't absolutely guarantee that there could not be some data breach that would leak them but I don't think it likely.