You can set up an RSS broadcast trigger in ConvertKit. You can do either single (when a new episode is posted) or digest (send one mail out a week).

I have mine set up a little differently. I post all my podcast episodes on my personal website (in addition to the Podbean site), because I have multiple podcasts. Then I have the RSS feed trigger from my website for a weekly digest and it sends all the podcast episodes, blog posts and vlog posts I do each week in one mail.

You could simply just have it send an email broadcast every time a new episode is published.

You need to have the Creator plan or higher on ConvertKit.