But to me that doesn't make much sense. What if I am a billionaire and the other person is very poor? It could very well be that the other person values the coffee a lot more than I do, but because I have so much more disposable income than they do I am willing to pay more for it. To me, the assumption should be something like the amount of money as a percentage of my total wealth that I'm willing to pay is equal to the utility of the good.

You're right, it doesn't make sense and it's even worse than you think, because even a given individual doesn't give the same value to something depending on whether they have it (and are asked a price to sell), or not (price to buy).[1]

[1]: https://evonomics.com/resolve-fights-reclining-airplane-seat...