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kotlinlang

i am looking for examples/suggestions on which libraries work best with kotlin-react and is multiplatform

Not exactly sure what you mean. Are you looking for MPP libraries in general? As kotlin-react is just a wrapper for js react and is not MPP

i am looking for a "thing" that lets me update data in react components, updating the UI
that is also usable in shared / jvm code for the project

I give you 99% that such things do not exist. MPP libraries in general are a pain and a major hassle to implement, so much better approach is MVP structure where model and presenter are in common code where views are implemented in platform-specific modules

The closest option for you would be kotlin-redux, which is mpp redux implementation