Why is it a gotcha? These kinds of treaties in general only care about the 'feelings' of nation-states, not individuals. The rule exists because countries often have some say in whether to extradite, and they make that decision based on known facts.

In this case, it's a statement from the US to the Bahamas about what they intend to do to SBF once he's in custody. If the US then goes on and punishes SBF even harder than what they originally told the Bahamas, the Bahamas might feel lied to. Think of it as a "we wouldn't have extradited if we knew he was facing the death penalty" kind of scenario. This rule thus exists to give the Bahamas a chance to remedy that.