(Using Blender 4.2.0)
The issue is that there is no Instance in the input geometry to capture the attribute. It has to be captured in the Point domain, then transferred to the Instance domain, as proposed thereafter.
Dark red nodes: Capture of the center
1. The original Capture Attribute node is replaced by a Store Named Attribute node set in Point domain.
Dark blue nodes: Construction of a lookup table collecting the center per mesh island
2. The mesh is duplicated as a Point Cloud with a Mesh to Points node, set such that vertex coordinates are replaced by the Island Index to which these vertices belong. Consequently, vertices of the same mesh island are moved to the same position. It is to notice that the named attribute "center" is transferred by this node.
3. The point cloud is collapsed into a single point per mesh island using a Merge by Distance node. The result is a point cloud such that the point of index $i$ is carrying the center of mesh island $i$ as a named attribute.
Dark pink nodes: Transfer from points to instances
4. To query the lookup table, the Index of the instance provided by the Translate Instances node is input in a Sample Index node.
Resources:
(Blender 4.2.0+)
