I would not use hide glue on this unless you are comfortable using hide glue.
Titebond and clamps are fine, I would also follow up with a cleat over the deformed section just forward of the back where it looks like multiple fractures are running from.
The finish is an entirely different story, as mentioned it takes skill to repair a patch like that and make it invisible
So maybe not stress about the cosmetics and just make it structural
Steve
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