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Is it possible to test views with integration tests (using Robolectric) or do I need to write UI tests? Could I in theory create a Binding for the View and unit test it that way?

Integration tests should support views and Compose. The link below has more information on it.
<https://developer.android.com/training/testing/fundamentals|https://developer.android.com/training/testing/fundamentals>

Unit tests won't support testing views, since you need an actual device/emulator, but integration tests do.