Learn Spanish (Latin America): Tenemos el hospedaje confirmado.

Hemos confirmado (using haber) is the standard present perfect, focusing purely on the action: "We have confirmed." Tenemos el hospedaje confirmado uses tener to focus heavily on the result or the state of things. It highlights that the task is complete and we are now in possession of confirmed lodging. It gives a strong sense of "it's sorted out" or "it's a done deal."

Would confirmado change if we were talking about reservations (las reservas) instead of lodging?

Yes, it absolutely would! This is a crucial difference between using haber and tener. With haber, the past participle never changes (e.g., Hemos confirmado las reservas). But in the tener + past participle structure, the participle acts like an adjective describing the direct object. If you used las reservas, it would be Tenemos las reservas confirmadas. Here, confirmado is masculine singular to match el hospedaje.

Could I change the word order and say Tenemos confirmado el hospedaje?

Yes, that word order is completely correct and very common. However, the order used here, putting the direct object (el hospedaje) before the participle (confirmado), is a great way to emphasize the state of that specific item. It sounds very natural when you are mentally checking items off a to-do list for a trip.