But any service/property that I “give up” I could theoretically have made money from in some way. Even in the cases the Talmud talks about, I could simply demand money from the other person in exchange for my concession.

A theoretical possibility, yes, but that is the distinction between something that is normally rented out and something that is not normally rented out. If you had put the courtyard up for rent before the customer arrived, that shows you intended to profit from it, and then it is fine. But if you were not planning to do that, and only when the customer shows up do you suddenly want money from him (for depreciation after he lived in the courtyard; some of the medieval authorities explain it only in that case), that is the trait of Sodom. Money you were not counting on in advance, but then an opportunity happened to come your way to squeeze it out of someone who needs it. And again, the trait of Sodom is not a legal-halakhic principle but a meta-halakhic one. Strictly speaking, the trait of Sodom is purely a moral matter; it is only that the Sages enacted a rule to compel against the trait of Sodom, meaning to bring morality into the law in this case.

So now I understand the criteria, but they still seem unfair. If I own a product and I have an opportunity to profit from it, why give priority דווקא to the person who has no claim at all to the product? That itself seems exploitative to me.

Because his need already exists now, whereas in your current situation there is no intention of profit. It is an asymmetrical situation.

My need to make money also exists, but I was not aware of the possibility of making money from the product.

That is not correct; we are talking about a case where you decided not to make money from your courtyard. You were aware of the possibility of doing so. If you were not aware of the possibility of making money, then perhaps it really would be permitted, because your original decision was based on a mistake.

So to sum up—people compel against the trait of Sodom when my desire to profit arises only once the other person’s need appears (and I suffer no loss from the use)?

Correct. And in light of your comment, I might add that you were also aware in advance of the possibility of making a profit and chose to forgo it. If you were not aware, then perhaps one could discuss whether you are allowed to try to profit once the matter becomes known to you.

Thanks.

Is price discrimination also considered the trait of Sodom?

I don’t understand.

Does charging a consumer a different price because I know that he specifically would be willing to pay a higher price count as the trait of Sodom?

Definitely not. He always has the option not to buy. If it is more than one-sixth above the market price, and there is a market price, then there would be overcharging here.