Curious, I cancelled mine yesterday because they messed up my billing and wouldn't/couldn't unsuspend it¹, so the CS person suggested to cancel and resubscribe. I did have to confirm about three times that this is what I wanted to do, but in no case was it hidden or not obvious.

¹ it was a bit of a mess, they first tried to bill an empty credit card, but only notified me after several attempts when prime was actually suspended. I added a regular credit card, but they don't conform to the new EU rules about authentication so it just got declined. Again, they didn't tell me they were even trying. So I added a SEPA account which is possible through the UI, but apparently they required a credit card. In the end I just cancelled, and re-signed up under the amazon of the country I live in (which is fairly new, hence not doing it the first time.) At least I get another free trial month for the hassle.*