Starting a plan involves two things: your payment going through at Stripe, and Stripe telling us about it. Those are separate, and the second one can be delayed.
If it was delayed past the moment you came back from checkout, we still believed you had no plan — so we sent you to the plan page. You had paid, and the product acted as though you had not.
Now the two are reconciled automatically. If your payment went through but the confirmation has not reached us, we check with Stripe directly and let you in. You do not have to do anything, and you do not have to try checking out a second time.