New phone, or a fresh install, and Wakeout is asking you to choose a plan even though you already paid? Your purchase is safe. You just need to restore it.
Open Wakeout. On the plan screen, scroll down and tap "Restore purchase". If you are already inside the app, open Settings, tap "Unlock Wakeout", then tap "restore purchase".
Wait a few seconds while Wakeout finds your plan with Apple.
Your new device needs to be signed in with the same Apple Account that made the purchase.
If you received Wakeout as a gift, sign in to Wakeout with the same account you used when you redeemed the code. There is nothing to restore with Apple.
Nothing found? Follow the steps in I'm subscribed to Wakeout but can't access the app.