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I've got hard time finding information about how to store settings in a desktop app... what would you recommend for this purpose?

Sorry, but it is not Compose related question. All operating system may have their own system for settings.
For Linux and MacOS good practice to use ~/.my_app_settings directories. But on MacOS you will need additional permissions.
Another way is to store settings in Application Content folder on MacOS.

ok, I understand. With Compose I'm often not sure whether it has something already on board or it's an entirely different thing. I guess I then should probably look for something generic related to Java

Compose is only focused on the UI, and it doesn't have an opinion on things like settings, DBs, app architecture/folder structure, etc. 

Multiplatform Settings has a JVM storage option, which wraps the standard Java Preferences <https://github.com/russhwolf/multiplatform-settings#platform-constructors|https://github.com/russhwolf/multiplatform-settings#platform-constructors>

thx! I've googled for general java solutions and I'll go with jackson-dataformat-yaml