A along time ago, I was
user58206 and I knew the novella mentioned the Birdman of Alcatraz, but I couldn't find it at the time. I recently decided to read it again and I found the passage that mentions that name.
Let me break it down.
The novella has a lot of characters, some of which didn't make it into the movie because they only play a small or sometimes insignificant role to the overall plot. For example, in the novella Andy had a cellmate for a brief time, but in the movie no cellmate is mentioned or shown, and according to the Warden, Andy lives in a one bunk Hilton.
One character is compared to the Birdman of Alcatraz, his name is Sherwood Bolton. He had a bird named Jake, and just like in the movie, he is set free before the character is granted parole. In the novella, the rest of the inmates find the dead bird after Sherwood has left Shawshank.
Red's quote (p.16):
He wasn't any Birdman of Alcatraz; he just had his pigeon.
The movie combines several characters to make it easier for the plot, for example, they're several Wardens who come and go in the prison and Andy helps all of them with scams, but in the movie, Norton is the primary antagonist.
Sherwood Bolton and his bird were written into the character of Brooks. We all know the story of Brooks from the movie, so I won't repeat it here, but in the novella it isn't as tragic.
There you have it, King uses the Birdman of Alcatraz as a comparison.
Is there any authoritative evidence that Brooks Hatlen's character was
based on Robert Stroud?
The character of Brooks wasn't based on anyone. The question should be, was Sherwood Bolton based on Stroud?
I don't believe so, because a direct comparison is made between the two characters. If Stroud was used as the basis for Sherwood, then I don't think King would have made a comparison like he did. Also, Sherwood's life isn't mentioned in detail, other than the small paragraph, that's pretty much it. Had Stroud been used as a basis, King would have written more about the character, enough for readers to compare the two characters.