Will the hotel price I see in the search still be the same when I go to book it?

Not always, and it is better to know that before it surprises you in front of a customer. Hotel prices come from live availability that can move from one minute to the next as rooms sell and as the hotel changes its rates, so a price in a search result is the offer at that moment rather than a figure that is locked for you.

That is why almost every hotel booking API has a checking step between the search and the booking. Before you take any money you send the chosen room back to the supplier, and it tells you whether that room and that price are still available or returns the new figure. A well built booking flow does this on its own and shows your customer the updated price before anything is charged. Small differences are common on busy dates, and also when the supplier quotes in one currency and your site sells in another and the rate has shifted.

If the room has sold out completely the API will say so, the booking cannot go through at that price, and nothing is taken from your customer. The usual way forward is to offer the next best room in the same hotel, or the same hotel from a different supplier if you work with more than one. Keeping your search results fresh, instead of showing prices that were pulled a long time earlier, cuts down how often this happens.

Check that your booking pages run that availability and price check right before payment, and agree with your staff what they will say to a customer when a price has moved.