Even after you cancel the Premium Plan, you can keep using the Premium Plan features until the period you have already paid for (or the free trial period) ends. That is why the Premium Plan is still shown for a while after canceling.
As long as the cancellation is complete, automatic renewal has been turned off. Once the period ends, no new charges occur and the Premium Plan simply ends. Please rest assured.
You can check whether the cancellation went through in the Google Play Store app: tap your profile icon at the top right → "Payments & subscriptions" → "Subscriptions". If the "Smart Planner" subscription is shown as canceled, the cancellation is complete.