Hi and welcome to the forum
My advice for Biscuit is to keep him indoors all the time at the moment. It is too cold to put a baby rabbit outside full time at the moment and also taking him in and out is not recommended as rabbits, even when adult, can't regulate a change in temperature very well. Once the weather improves in a few weeks, if he is to live outside, then I would transfer him outside full time.
I would think that it's likely that he is confused at the change in his accommodation and that is why he saves his pee for the place he recognises as home. When you transfer him to his new hutch outside, you could also place some of his soiled litter there, so it feels like it's his territory.
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