> I've never seen people using UTF-8 deal with a code unit stage. They parse directly from bytes to code points.

Well, that's probably because in UTF-8 code unit is byte :)

Quoting https://en.wikipedia.org/wiki/UTF-8:

> The encoding is variable-length and uses 8-bit code units.

By definition, code unit is a bit sequence of a fixed size which can form code points. In UTF-8 you form code points using 8-bit bytes, therefore in UTF-8 code unit is byte. In UTF-16 it is a sequence of two bytes. In UTF-32 it is a sequence of four bytes.