I downloaded the app and paid for a subscription, but the paid-for version isn’t showing up on my phone (or other devices).

If you have an active subscription, you may need to Restore the subscription. Follow these steps: Open the app, click on the menu icon in the top left corner, then click “Your Settings”, from there, click “Subscribe Now” and select “Restore purchase.”
Apple and Google Play use the credit card you have on file with them for your app purchases. If you’re unsure whether payment went through, neither Apple or Google Play will allow you to purchase the same app twice. They have a fail-safe system, so you cannot possibly purchase it more than once.
If none of these steps work the phone may need to be reset. Try turning your phone/device off and on. You can also try deleting the app and re-downloading it.