Personally, I doubt Man United to sign Mbappe. Man United may have the money to sign him, but Mbappe should prioritize Real Madrid over Man United. Real Madrid is his dream team and Real Madrid offers a bigger chance to win any top trophies. Specifically, Real Madrid is a perfect team for Mbappe if he dreams to win UCL trophy. So, he should assume to have a better career in Real Madrid. Well, because of these reasons, I'm very doubtful if Man United can change Mbappe's mind. Since the chance is likely very small, I think Man United is better to look for another striker.
In addition, Real Madrid constantly monitors Mbappe's situation in PSG. If Mbappe has the intention to leave PSG, Real Madrid must be the first team to know it. So, Real Madrid is likely leading the competition to sign Mbappe.
For Manchester United it is clear that they will definitely try to be able to bring him in, because after all Ten Hag wants the best for his club. But indeed on the other hand this can be something that is not profitable for Mbappe because, as you said, there will be very little chance for him to win some of his dream trophies in various competitions. Mbappe must be able to think about the future for his career, the opportunity is huge for some new achievements if he chooses to join Real Madrid. I hope he knows what he has to do for the benefit of his future career.