First, I must emphasize that you should use
UNIQUE when you need the uniqueness check, not for performance considerations.
That said, here are the small performance considerations:
INSERT checks for uniqueness before acknowledging the insert. This slows down the response time (a little) for
INSERTs. A plain
INDEX is delayed and does not actually get performed until later. See "Change buffering". This speeds up non-unique index maintenance (a little).
SELECT, when using a non-unique index will (unless something else stops it), will read rows until the value is different. With a
UNIQUE index, it knows to stop after one row is found. (Again, a minor performance difference.)