Where is SIGHASH_TYPE serialized in SegWit?
Is 1 byte appended to the signature in the the same way, but in the witness data rather than the legacy part of the transaction?


Yes. The signature serialization (which includes the sighash type) remains exactly the same.

Look at the first example in BIP 143, the generated signature (before serialization) is 304402203609e17b84f6a7d30c80bfa610b5b4542f32a8a0d5447a12fb1366d7f01cc44a0220573a954c4518331561406f90300e8f3358f51928d43c212a8caed02de67eebee. When it is serialized, it becomes 47304402203609e17b84f6a7d30c80bfa610b5b4542f32a8a0d5447a12fb1366d7f01cc44a0220573a954c4518331561406f90300e8f3358f51928d43c212a8caed02de67eebee01. Notice how when serialized there is an additional byte appended to the signature; that is the sighash type.