This may be harsh but I'm not keen on the idea of spending big money on him.
I can't recall many players who were past their physical prime so young that they had to completely change their game. And to be fair, he's adapted his game incredibly well - his passing, creativity and decision making on the ball is top notch. The issue is now he's a specialist in the sense he really needs a certain set up around him with pace either side who can run in behind for him to slide his passes to.
He drops very deep and I'd worry he'd be crowding Bruno's space, and Bruno is going to work best with a striker who's making runs to pick out, rather than dropping deep into his area. Kane's lost a lot of his traditional threat of challenging centre backs and running in behind the opposition defence.
He also looks very laboured in his pressing these days if that's what you want from your striker, I don't see him suddenly returning back to a more energetic style of play in his 30s.