Even if it seems like a coincidence, it could be a meaningful coincidence within the dramatic structure of football. Just like life's sense of humor. Bayern are already the best in the Bundesliga and it shouldn't be difficult for Kane to win a trophy with Bayern. But the biggest chance was for Tottenham, who sent Kane away.
Kane's departure triggered a structural change at Tottenham, leading the club to look for a Kane-less game and a more balanced team. As fate would have it, Tottenham achieved much better results without Kane, and the team shaped itself around his absence after his departure. This has resulted in a more collective, pressure free, team oriented team. This restructuring could bring success again next season.
How can they be considered significantly better if they only finished 17th in the Premier League? They were only helped by the Europa League trophy as otherwise they wouldn't have qualified for next season CL and their journey in the competition last season was relatively easy. From the league stage to the semifinals they played against teams below them and in the final they faced a Man Utd side who were also struggling in the league. So Kane departure doesn't change anything; it's just a fluke that means nothing and I doubt Tottenham will be as lucky in the new season.
Yes, Tottenham may not be as fortunate as last season, for a simple reason, the club fired Ange Postecoglou. Thomas Frank will be faced with a much tougher task, ensuring his squad performs consistently in the Premier League and Champions League. If the adaptation process is slow, or disrupted by injuries, I'm sure Thomas Frank won't be as resilient as Ange Postecoglou in dealing with the pressure. Meanwhile, Tottenham success in the Europa League last season, and their failure in the Premier League, actually had nothing to do with Kane.