I think it bears repeating, though some forum members may be tired of hearing it, that booking and all the other travel site apps do not have access to all of a place’s beds. When booking tells you there’s no availability it only means that they don’t have access to any more rooms. They actually do tell you that now, after some governmental entity told them that it was a deceptive practice to say “there is no availability” when the truth is that “there is is no availability on our site.”
It is always a good idea to check directly with the hotel/pensión/albergue directly. Some forum members do it because it is a way to give a few more euros to the owners of small places who have to give a chunk to booking, but whatever your reason, you will frequently find that in fact there are rooms when booking tells you there are none.