Hotels do also, based on nationality. I’ve had to implement something like this when working at a hotel aggregator (like Trivago but not them). You would start the booking process from let’s say Germany, but you have a Romanian passport. You would get German-people prices (which are lower) based on your IP, but you were asked about your travel documents. We had to do a request with your password to the seller which would reply that the room was already booked. You would get a message to start the search again, but now we would do it with your actual data. You would either get the room listed again at a higher price or not at all.
I use a hotel aggregator too (Booking , Agoda primarily) and my experience has been that it does not make any difference at all what nationality I've. I see exact same price whether I use incognito, another browser, device, or even when my partner (living in a different country and holding a different citizenship) searches and books a hotel.
So, let’s jump to the step where you found your hotel and you want to book. We would pre-reserve the room and you would get a screen where you had to input your data and pay. Among the data, you would be asked about your passport or travel documents and you would have to select the country that issued the document. Upon send, we would send an API request to confirm the booking, but if the portal didn’t like your actual nationality, it would reply that the room is no longer available. We would then have to tell you to start the search again, but this time tell the portals your actual nationality. They would either choose to give you the room at a higher price or not at all.
Anecdotally, Booking does the same thing. I don’t know if with higher prices but definitely with availability. We had hotels show availability for my account where the address is in Germany but not on my wife’s, where the address is in Romania.
My best anecdote is when we were transiting Hungary and booked an apartment in Budapest with my account. We would get there after the reception closed because of traffic so we called and ask what we can do. The lady says that we can send copies of our passports per email and she would check us in and leave the key with the building’s security guard. We send her our Romanian passports and in less than 15 minutes receive a reply that the apartment is no longer available because a pipe burst in there (presumably the pipe burst after finding out Romanians will stay there for the night)