I upgraded, but my OSX todoist does not seem to get that. Even after logging out and in, or restarting it, it keeps saying "Upgrade and get more done". It also does not sync correctly.
Please tell me, are you certain that you're logging into the same account in the app as on the web? If it neither recognizes Premium nor syncs your data, it sounds like it may be a different account. For example, if you've created your account manually and then used the "Sign-Up with Google Account" option, this could have created a separate account.
If that's not the case, please try to log out through the "Logout" option in the TD menu at the top (not from within the app), then clear Safari's cache (as our app runs on Safari's engine) and then log back in using the same credentials you've used when posting this message as the account you're logged in right now is indeed Premium.