Wright definitely does not advocate soul sleep. He thinks that the intermediate state is some sort of restful, conscious existence in the presence of the Lord (hence the use of ‘paradise’ as a description which wouldn’t make much sense in terms of soul sleep), until the day of resurrection when we will be re-embodied.

To quote from Surprised by Hope: “all the Christian dead are in substantially the same state, that of restful happiness. Though this is sometimes described as ’sleep’, we shouldn’t take this to mean that it is a state of unconsciousness. Had Paul thought that, I very much doubt that he would have described life immediately after death as ‘being with Christ, which is far better’. Rather, ’sleep’ here means that the body is ‘asleep’ in the sense of ‘dead’, while the real person - however we want to describe him or her - continues.

… it is a state in which the dead are held firmly within the conscious love of God and the conscious presence of Jesus Christ, while they await that day. There is no reason why this state should not be called ‘heaven’, though we must note once more how interesting it is that the New Testament routinely doesn’t call it that, and uses the word ‘heaven’ in other ways.” pp.183-184

Explicitly, Wright states that “the Christian dead are conscious” (p. 185). This is from the section in the book on ‘Paradise’, pp. 183-187

The Bible provides little information on what this state is. Compared to our bodily existence, it is like sleeping. The believers will be with God. I guess the reason why there is so little information is that ultimately it’s not that important, compared to our final bodily resurrection in the New Heaven and the New Earth.