App bought AFTER May 2020
If you bought the ad-free version of the app via an IAP (In App Purchase) or subscribed to Podcast Addict Premium, then installing the app from the Play Store account used for the payment will automatically restore them.
App bought BEFORE May 2020
You will need to open the app Ad-Free/Premium screen and use the link that allows you to Restore the old purchase
Another solution can be to open the Play Store app and then go into Library / Family Library using the navigation sidebar. There you should be able to find and install the Donate app.
If your device is running on ANDROID 13 or more recent, the Play Store might be blocking access to the Donate app (purchases made before May 2020).
As a workaround, you can open The Google Play Store app, then press on Budget & history and scroll down until you see the 'Podcast Addict Donate' row. Press on it to open the Play Store app page and then install the app.