What would the ruling be לגבי drinks in a minibar that costs extra? At the beginning of the vacation the hotel owner fills the small refrigerator in the room with drinks, and at the end of the vacation the guest is charged according to which drinks are missing from the fridge. Would it be permitted to consume a drink from the refrigerator on the Sabbath? Here there is no recording of a room number, because the drinks are already in the room. The question is whether there is a commercial transaction involved.

In my opinion, no. This is not a normal way of making a purchase.

Regarding the problem of writing things down—does it make a difference whether he is Jewish or a gentile? In many hotels the employees have ways to preserve this information without desecrating the Sabbath, such as putting on stickers and the like. Would that change anything if I know he will most likely write it with a pen, but he also has another option? And in general, why is it my problem that he writes it down? He is doing it for himself so he won’t forget that I owe him money, no?

Without the writing, he would not sell it to you. Your reasoning doesn’t sound plausible to me.
If he has a way to do it without writing, that is indeed a relevant argument. Then only the issue of the commercial transaction remains, and that can be discussed. It isn’t unequivocal.