Google

i never knew youtube podcasts were a thing either

It was simple and easy to use. I've since switched to AntennaPod, which has some quirks, but it's filling in nicely. My only gripe w/ Google Podcasts was there wasn't a way to export my podcast list at the time I switched.

If it helps someone reading this, there now seems to be a method

Credit: Podcastaddict.com:
Exporting Your Subscriptions from Google Podcasts

1. Initiate Export from Google Takeout

   Navigate to Google Takeout. In the list of Google services, select 'Google Podcasts'. Follow the prompts to create an export of your Google Podcasts data. Choose the OPML format for ease of use with Podcast Addict.

2. Download and Extract Your Data

   Once Google has finished preparing your data, you will receive an email with a link to download a zip archive. Download the zip archive to your computer and extract it to find the OPML file containing your podcast subscriptions.

3. Transfer the OPML File to Your Device

   Connect your phone to your computer via USB and copy the extracted OPML file to a convenient location on your phone. Alternatively, you can email the file to yourself and then download it directly to your phone from your email application.