Unfortunately there’s no way to currently embed a whole Podpage site into another site. The closest you can come is make your Podpage site a subdomain of your current domain name.

How would this work?

Let's say you have an existing website at www.your-domain.com and it contains a single page for your podcast at www.your-domain.com/podcast. There's no way for you to replace that page with your Podpage, because podcast is a complete website with lots of different pages and sections. However, there is a way for you to create a podpage that would

while your existing site is hosted at www.your-domain.com, your Podpage site can be at podcast.your-domain.com, and you can link to the other site from the navigation bar.

It’s not exactly what you’re looking for but it’s how users are currently doing it. Hope that helps!