Adding Safari extensions to the apps made with Sonoma's "Add to Dock..." feature

As far as I am aware, adding Safari extensions to the apps made with "Add to Dock..." feature is not possible at the moment, correct me if I'm wrong. I believe this new macOS Safari feature is really useful and I'm already using it for couple of websites I use frequently.

However, the lack of Safari extensions in these apps is holding me back from using this feature for some websites. I'd love to see Apple introduce the ability to add Safari extensions to these apps.