No, Android doesn’t allow embedding parts of apps directly within a web browser.
As you alluded to, if the app has an integration with a Smart Home platform that we support, you may be able to integrate it directly. Or if the app has an API, you might be able to integrate it that way. For example, there’s a community developed Spotify Custom Tile.
Otherwise, some people use Hyperlink Tiles so they can tap a tile to open their desired app, then back out of the app to return to their dashboard… or if you’re using a kiosk app like Fully Kiosk, you may be able to have it automatically return to your dashboard after a period of inactivity.