Manchester United and Leverkusen are not the same. The two clubs have different scenarios and different goals. At Leverkusen, ten Hag will not have the big funds to buy players. So ten Hag will have to try to find talented players. On the other hand, Manchester United had a lot of star players. Managing so many star players was also difficult for ten Hag. Ten Hag will not face this kind of problem at Leverkusen. My guess is that Leverkusen will not fight for the title next season. They will try to keep their performance stable and secure a ticket to the Champions League.
Because Leverkusen's performance was quite good last season, I think Ten Hag's task is at least to maintain their performance in the Bundesliga. An added value if Ten Hag gives a surprise with tight competition with Munich or other strong teams in the Champions League.
Leverkusen's situation with United is clearly different. Ten Hag must also be under pressure when handling Leverkusen, because if their game is chaotic, it will be highlighted by many parties. Ten Hag must perform well.
The times are over that Leverkusen is trying to end the season in second place and everyone is happy. They have now got to know how it feels to win titles and to compete on the highest level. Last season was ok for them, I don't think they themselves would call it a good season. They got eliminated by a third league club in the DFB Cup and they didn't do much in the UCL.
In the next season their main goal will be to compete with Bayern for the title while they have now lost some of the strongest players they had. It won't be an easy job for ten Hag to fight all the criticism that came up before he even got started there. But this has mostly to do with what he left behind in Manchester, which was catastrophic as the club had a historically bad season.
Despite that bad performance in Manchester, he again gets the chance to coach a great club. Leverkusen has lots of potential and now it depends on him to at least maintain that level, but as I said I think the bosses expect more.