Is there any way to download the history of played episodes in Google Podcasts? Or in other words, is there any way to get the data from Google Podcasts? Some API or something?
The only way to download playback history from Google Podcasts I found is to use Google Takeout (this link can be found in the "More options" section of the My Activity — Podcasts page, where you can also see your subscriptions).
If you click the "All activity data included" button, you'll be able to specify which Google app you want to export data form. Click the "Deselect all" option to remove all apps, then check only the Podcasts entry.
You can also select the "Multiple formats" button to pick what format you want for your data export: HTML or JSON files (the default is HTML). The information in the files includes the activity type (playbacks, searches, etc.) and the corresponding date.