It's a very common thing. A very unscientific quick search in Google Books led me to the oldest example I could find in a minute or two being a mention in The Dublin Review in 1844 reviewing a book on the correspondence of Edmund Burke talking about the loss of material that would have been indispensable for an authorised biography. It's very unlikely to be remotely the oldest use of the term.

And that mention also gets to why authors often seek authorisation and why subjects often authorise them: Authors gain access to the subject and/or often their material, while the subject or their estates gains some control over how they are portrayed.

I know what you mean, but there is a reasonable distinction to be made especially for living persons. An "authorized" biography would be something like what Isaacson does, where they get exclusive access, anecdotes, and importantly confirmation or denial of certain facts or stories.

An "unauthorized" biography is not necessarily suspect but it is kind of a subgenre. Consider the difference between Isaacson's Musk biography and the work done by Kate and Ryan for Character Limit (https://www.amazon.com/Character-Limit-Elon-Destroyed-Twitte...) - not exactly a biography but the legwork is fundamentally different, reportorial or even adversarial where the narrative gets challenged, as opposed to accepted by the "authorized" Isaacson.

Authorized/unauthorized simply describes whether the subject works with the author or not. It's just the common terminology for it.

Technically, a wikipedia page of a [living] person is an unauthorized biography!

But we'd like to think the crowdsourced editing process gives it some more trustworthiness than a random person self-publishing a book

If a biography is authorized, then you can interview the subject, and in some cases those interviews provide a lot of the material. Walter Isaacson's biography of Steve Jobs was like this, for example.