If the definition/denotation of the word "unique" is "being the only one of its kind; unlike anything else," how can that unique something be extremely the only one of its kind, more than unlike anything else?
Yes, yes, yes, I understand that what the writer/speaker means to convey is that the unique thing is rare to the highest degree possible. 😊 That "very" addition is just unnecessary (and, literally, ridiculous) emphasis.
In speech, the phrasing is nails on a chalkboard to my ears, but forgivable. A small annoyance. When it appears in the written word, however, it's a disaster, not the least because it's usually accompanied by many other instances of lazy writing and slipshod editing.
Show the reader what, specifically, makes the thing especially singular. Original writing is, after all, very unique.