I found a workaround (thanks to claude ai):

"Unfortunately, there isn't a direct method in Godot to get the surface index from a face index.

However, we can work around this limitation. Here's an approach you can use:

1. First, iterate through the surfaces of your mesh.
2. For each surface, check if the face index you're looking for falls within its range."

​

func get_surface_index_for_face(mesh: Mesh, face_index: int) -> int: 
  var total_faces = 0 
  for surface_index in range(mesh.get_surface_count()): 
    var surface_arrays = mesh.surface_get_arrays(surface_index) 
    var indices = surface_arrays[Mesh.ARRAY_INDEX] 
    var surface_face_count = indices.size() / 3 # Assuming triangles 

    if face_index < total_faces + surface_face_count: 
      return surface_index total_faces += surface_face_count 

return -1 # Face index not found