How to extrude polygon from X-Y until intersection with inclined plane

The considerations are already very detailed.

To recommend the best way at the first go is certainly difficult.

Have you seen the example of the cut in the
Collection of examples from discourse.threejs.org ?
https://hofk.de/main/discourse.threejs/2018/index2018.html
PointsGroupingCutPlane - @prisoner849 author (with more links in the source code)

https://github.com/mapbox/earcut produces triangles of very different sizes. The algorithm I use results in smaller triangles, but may not be important for flat structures.
Addon for triangulation of implicit surfaces/ forms with holes

Some flat surfaces (test, still unfinished, use the slider) https://hofk.de/main/threejs/1TEST/InnerGeometryTriangulation221219.html

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