That’s correct. You don’t need to do anything else.
When you cancel a subscription, its status changes to “Cancelled Payments”.
That means that the subscription will expire at the end of the current billing cycle. It will not be renewed and you will not be charged ever again.
If you’re on a free trial, you won’t be charged at all.
However, you still have access until the subscription ends.
When it ends, its status changes to “canceled” and you lose access.