Finding level 3 islands in OSM data?

I recently had the joy of finding a level 3 island (Way: 1233009406 | OpenStreetMap) on aerial imagery, an island in a lake on an island in a lake on an island.

It’s not too far away from me, so I’m planning to do an expedition to survey it which will include a refreshing little swim in January.

Finding such islands in OSM data seem algorithmically straight forward, but the idea of downloading a full planet file scares me a little. I’m also not fluent enough in Overpass yet to find such objects that way.
Has anyone else here tried finding recursive islands before?

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