DG Imagine the furore if the UK extradited a Brit to the USA under promise of no death penalty ... and then the USA reneged on that agreement,
I think I would have to imagine - not being a lawyer I can't be definitive, but I really can't recall a case where someone was extradited to the US under an agreement "not to seek the death penalty" and that agreement has then been reneged on. (Such a scenario was written into a "Law & Order" years ago, interestingly enough, which is how I came to know about it ...).
Certainly a casual Google doesn't throw up any cases.
I know that if I were representing a client arraigned for extradition to the UK, where I was in the world, I would happily use the current willingness of the UK to apparently renege on a treaty as fodder for their case. A lot would hinge on whether it became real or not - so it's all down to whether the bill jumps its commons readings, Lords readings, and whether Her Majesty is happy to sign it, knowing if she does, then her place as "Leader we'd trust to look after the handbags" (after Elton) is gone forever. Who knows. Maybe after a lifetime of impeccable service even Lizzie Two wants to Break Bad for a bit ?
When we called them "The Bad Boys of Brexit" (and that does have weirdly homo-erotic undertones now I type it) it was a retrospective description, not an aspirational challenge.