Just Upgraded to macOSX Catalina -- How Do I Sync My Computer's Podcasts and My Apple TV's?

I always "managed" my podcasts through iTunes and played the pods on my Apple TV through the "Computers" icon (like I played my music) -- I never used the Apple TV Podcast app.

Now that iTunes went away my podcasts are on my computer with the Podcast app 1.0.0 (1425.5)

On my Apple TV there are no longer Podcasts on the "Computers" but the Podcasts under the Podcasts app don't sync with the stuff on my computer. When I open the Apple TV Podcasts there are pods that I once subscribed to but deleted years ago. There are even podcasts shown that no longer exist. And the ones that I do want are not up to date -- the most recent episode is months (sometimes years) old.

How do I get rid of the old junk podcasts on my Apple TV and get the same up-to-date information as I have on my computer?

Thanks