Hi Laura!
Even though there isn't an embed option in the share link on the StoryMap (like there is with Story Maps Classic), you could still load your StoryMap into an iframe and embed that into your website. Here's a really simple example HTML embed code example:
<iframe width="800px" height="800px" src="https://storymaps.arcgis.com/stories/c10f1596870e4e788d3f687935bfd1ae"></iframe>
This is the same kind of HTML embed code that's used by the Story Maps Classic. In fact, I grabbed the embed code from one of my classic Story Maps and just switched out the URL in the HTML to use this new StoryMap instead.
If you haven't seen it, there's also a blog post that talks about tips and tricks for embedding Story Maps in websites:
https://www.esri.com/arcgis-blog/products/arcgis-enterprise/uncategorized/embedding-story-maps-in-we...
While this blog is geared towards Story Maps Classic and some of the functionality discussed does not work with the new StoryMaps (such as the tip about minimizing the UI), it's a really good resource for general tips/tricks for embedding your content in a web page.
