I'm a person that really likes running and a couple of years ago, I bought myself an Apple Watch which serves as an activity tracker and music delivery system (I'm using bluetooth earbuds).
While running, I like listening to several podcasts. On my iPhone, I'm subscribed to several podcasts in the Podcasts app (by default available on iOS). There's a very nice (automatic) synchronisation with the Apple Watch which allows me to also listen to podcasts on my watch as well.
However, after listening to a podcast, the podcast is always automatically deleted from the watch which doesn't give you the benefit anymore to listen to it twice. I can also not redownload the episode to it. I searched everything and I even asked help to the Apple Community (see here), but I never came to a decent solution.
So I switched to OvercastFM. This app states in the documentation that you should be able to keep the podcasts on the watch after listening to them. However, I tried that but it didn't work. So I asked them for help ... and I never got an answer - which I still believe is a pity.
So the next app I tried was Pocket Casts. To get to the feature I want, I had to take a 'plus' subscription (so it's not free unfortunately), but finally, I found the app which solves my issue. On the Apple Watch itself, I can now easily choose which episodes I want to keep offline. There's still the annoying factor that the podcast is automatically deleted on the watch after having completely listened to it, but you can easily redownload it. Keep in mind that's better to disable "bluetooth" on the watch while downloading podcasts so that the watch is forced to use the WIFI network. I've noticed by default, it uses Bluetooth and some podcasts (for example of 250 MB) really take ages to get downloaded ...