Does this mean all desktop integrations have now migrated from alpha and are available on stable releases?

The post isn't 100% clear on this.

I tried out Flutter a while ago, and it's really promising as the only really viable alternative to the JS/browser stack for cross platform GUIs.

Dart is not terribly inspiring and lacks the appeal of other new languages like Kotlin or Swift, but it's fine; as in: boring/easy to pick up and good enough for frontend, although somewhat sluggish.

ps: I personally don't see the design of Flutter Web as viable for production apps, so if you need Browser support, a JS stack will remain the only solution, at least for a few years.