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

Google implemented a rather confusing feature which cancels (and refunds) your purchase when you uninstall the app within 15 minutes after 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 you instead for instance delete the paid version of the app instead of the free version after the purchase by mistake, your purchase gets automatically cancelled and you'll have to re-purchase the app again. 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.