Manchester United and Leverkusen are in a completely different situation. Manchester United's decline cannot be blamed solely on their coach. Their management has a role to play in Manchester United's decline. Also, the bonding between the players was weak.
However, I also think that Leverkusen could have taken on someone more experienced if they wanted to. Ten Hag's biggest failure with Manchester United was that he bought several players at very high prices. And Manchester United wasted a lot of money. However, he cannot do that with Leverkusen. Leverkusen will not create a large fund to buy players. So Ten Hag will have to try to strengthen this squad.
Ten Hag was quite successful with Ajax. And this is probably why Leverkusen gave ten Hag the responsibility. The situation of Leverkusen and Ajax is very similar. So Ten Hag has a chance to succeed with Leverkusen. Manchester United had a lot of star players. It was difficult for Ten Hag to manage star players. Ten Hag will not face such problems at Leverkusen.
It is far from certain that he will not have problems with players in Leverkusen, because he had problems with a player (I don't remember the name, but the situation is exactly the same as in United) in Ajax and he got rid of him. TENHAG apparently likes to play the game "I'm the big boss" but it doesn't work in big clubs. Leverkusen (with all due respect to Ajax) is a different level and here I expect problems again.
Plus his coaching qualifications also raise questions - as you correctly wrote, he made expensive acquisitions, i.e. he got what he wanted, but in the end these players did not justify the costs.