Is there a way to embed a browser inside of a desktop compose app?

I believe there's an example in the repo.

See comments on https://github.com/JetBrains/compose-jb/issues/1147

I think the team has deprioritised CEF (Chrome Embedded Framework) integration for the short term to work on other features, but they'll surely get back to it. I think a workaround for now is to show a Webview via Swing/JavaFX (noting that the latter isn't included in JRE anymore if I'm not mistaken), but haven't tried it

Using jlink to create an all-in-one executable will make it easy to ensure JavaFX is present in your application.