Split curve with another curve

In Polygon, you can use tinyCAD Mesh Tools Addon (default Addon)
https://docs.blender.org/manual/en/latest/addons/mesh/tinycad.html

In curv, you can use curvecad (additional installation addon).
※ Available on Blender 3.6

Bezier Curve CAD Tools - Coding / Released Scripts and Themes - Blender Artists Community

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