I think the answer from @MarkusvonBroady should be sufficient for your needs. Here is just an additional / alternative version: in Blender, a curve object consisting of several splines can have different Cyclic settings under Active Spline in the Curve Properties for each spline. Of course you can set them individually in Geometry Nodes as well, but it seems not many people know that even without GN, a curve does not necessarily have all cyclic or non-cyclic splines.
So, if you get rid of the Set Spline Cyclic node (or mute it), the splines will use the individual settings given in the Curve Properties. In the follwoing example I simply duplicated the spline a few times in Edit Mode and set some of them to Cyclic and some not:
Now you could use a Sample Curve node set to Boolean instead of Sample Index, because this way you can not only get the Cyclic information of the spline determined by the Curve Index, but also the position of the respective spline (in this case it is the location of the first control point).
This can be used e.g. to switch through the individual splines and show there Cyclic status and even place the text next to the spline in question. As I said, this might not be needed, it is just an additional way of retrieving information.