Ten Hag has indeed not made great achievements for Man United but I think he has made quite a significant change. So if he is still trusted to handle Man United for the following seasons, Man United will be a serious challenger in the Premier League. Man United need to get a new striker this season but I don't think they will be able to sign Harry Kane because the price is too high for Man United. Rasmus Hojlund is a pretty good option and the signing could be a great investment for Man United.
Kane wants to play for Bayern and Bayern remain hopeful of getting Kane. Kane's move to Manchester United seems unlikely to me, this is a rival team and even more so I think that he himself will not want to play for Manchester United. If this off-season does not work out with this transfer, then next summer his contract expires and then he can go to Bayern as a free agent, so Tottenham should also be interested in selling him before that time.
Thus, at least Bayern Munich and Manchester United might be able to compete to be able to bring in Kane at this moment or in the upcoming transfer market. But, I personally don't really care where Kane will go, but one thing I hope is that at least Kane really has to leave. Because playing at Tottenham also didn't provide any achievements for Kane so yes, leaving is the right way for Kane. But regarding Erik ten Hag, I personally have considered him successful in making Manchester United better last season. What's more, Erik ten Hag also still has a contract until 2025 and of course, if Erik ten Hag can be consistent every season to make Manchester United strong in the top zone, then surely Erik ten Hag deserves a new contract later.