Being a coach in our times is not among the jobs I would decline because of the pressure and the danger to lose my job today or tomorrow. If they sign their contracts and get sacked, life goes on on the Bahamas or Maldives or Mallorca or wherever their holiday mansions are. They don't care. Bayer Leverkusen is backed by pharmaceutical giant Bayer and money has never been a problem for them, especially now that they sold Wirtz and Frimpong. I think ten Hag will get the money he wants, at least for most players. The finances shouldn't be the reason he can't be successful.
Manchester United has also shown that it knows how to secure funding for transfers and how to get the players it needs. If I'm not mistaken, during the few seasons that Ten Hag has been the manager of Manchester United, he has signed more than 11 players. In fact, you could say that he completely rebuilt the entire squad through transfers. And I agree with you that Bayern is a club that has never had problems with money, so if necessary, Ten Hag will get the funding and the players he believes he needs.
The budget at Manchester United isn't the same as the one at Leverkusen, of course. Expectations aren't the same either. For Ten Hag, who didn't succeed at Manchester United, Leverkusen will be a new challenge and a new marathon. I believe he'll be more successful than his Manchester United days, but still won't be able to shake Bayern Munich's throne. Ten Hag and Leverkusen need each other. We'll see how Ten Hag gets through this period.