Yes they do. Google Pay or Google Earth are using Flutter. They also contribute to Kotlin Multiplatform and use it for Google Workspace (gmail, drive, etc)
Flutter and Kotlin Multiplatform are two different frameworks. Flutter is mainly for cross platform UI. KM is mainly for common-core (or common business logic). My point still stands that these are all bloated and ugly.
Google products are an absolute mess. They create android, KM, and Flutter for mobile development. They also created MLKit, MediaPipe, and TensorFlow for AI. They're all over the place with their solutions
Not Java, but close. With Kotlin, there is a version of Jetpack Compose (Android UI framework) ported for the Web. It's still experimental. Produced size is a bit too much (because of Kotlin/JS not being super optimized yet).
Vaadin has been around for a while now. I don't know how people feel about it. There is still some room for them on the market. It's "just" a backend service (Spring/VertX/etc) + a UI library (Vaadin's one/etc). It could look like Next.js but for JVM languages.