I deleted the paid app by mistake and I'm asked to buy the app again

Google implemented a rather confusing feature that cancels (and refunds) your purchase when you uninstall the app within 15 minutes of the purchase. The logic behind this behavior is that you have 15 minutes to evaluate the app, and if you dislike it and uninstall it, you get your money back automatically.

However, if, for example, you accidentally delete the paid version of the app instead of the free version after the purchase, your purchase gets automatically cancelled and you'll have to re-purchase the app. Since you get refunded for the original purchase, you will never pay twice for the app. To see all your transactions and refunds, you can check https://pay.google.com.