1. To roll commitments up the trie recursively: we commit to scalar field elements. To use commitments as values of another commitment, we need a map element -> scalar field. This is not to_bytes(), but is map_to_field(). It uses x/y in extended coordinates, and converts base field to scalar field via integer reprs.
2. To  save the commitment in the trie: in this case, we need full and correct ser/des. Actually, to_bytes() seems good enough, as with the x affine coordinate, we can retrieve an equivalent point. This is implemented in from_bytes().