Could you please describe the data you have to support the modeling you are interested in and provide definition of the connectivity index as it pertains to your specific use case? That will drive potential solution(s). For example, do you already have the stream network and locations of culverts you are interested in replacing in vector format or are you starting from digital elevation model and want to derive streams in the process.
If you already have vector representation of the stream network and points of interest on it, you can use tracing capabilities in ArcGIS Pro to identify impacts of barriers on the upstream/downstream connectivity. If you do not have the stream vectors but have DEM, you can derive the streams from it using Arc Hydro tools and then use the tracing to evaluate the culvert removal impacts or alternatively, use watershed delineation at points of interest to evaluate the impacts.
Arc Hydro tools do not have an explicit tool to create the “connectivity index”, but depending on your specific requirements, it would be possible to create a tool for it (if necessary supporting data are available).
