I am also uncertain as to what is referenced. Maybe the links below will help sort things out.
Seville - Royal Alcazar includes the Cuarto Real - "upper room" in this link. If this is being considered - having visited March 2024, my opinion is a "yes". Try to get a ticket for this area. Quite impressive. You do need to book in advance as they sell out. On the same property as the rest of the Alcazar site. Audio guide provided and visitors are escorted by a "guide" (really a leader with not much commentary) and guards to move from room to room. https://alcazarsevilla.org/prepara-la-visita/
Madrid - Two different venues, the Royal Palace proper and the Royal Collections Gallery. Two entrance fees. The buildings are next to one another.
The Palace is impressive. Highly recommend a visit. https://www.patrimonionacional.es/en/visita/royal-palace-madrid
I was surprised that I found the Royal Collections Gallery (a fairly new venue) a bit cold. Not that the collection wasn't extensive, but as a collection of art and decorative items, I did not enjoy it nearly as much as the major Madrid art museums and the Lázaro Galdiano Museum for fine art or smaller museums such as the Museum of Romanticism for decorative art. https://www.patrimonionacional.es/en/actualidad/galeria-de-las-colecciones-reales