Can a cat house help rescue cats feel safer indoors?

About six weeks ago I adopted an adult rescue cat who had apparently spent most of her life outdoors before entering foster care. Since bringing Milo home, she has been eating normally and using the litter box consistently. But she still spends most of the day hiding under my bed or behind furniture whenever there is movement or noise in the apartment. She only seems fully relaxed late at night when everything is quiet and there are fewer distractions around her. I tried making the environment calmer by moving her food and water into quieter areas, limiting loud sounds, and giving her more space. But she still seemed anxious and constantly alert during the day. A volunteer from the rescue group suggested trying a covered cat house so she could have one enclosed space that felt predictable and secure instead of hiding in random corners where she still appeared tense. While looking online for ideas, I noticed a surprising number of indoor pet shelters and enclosed hideouts online designed specifically for shy rescue cats and anxious indoor pets adjusting to new homes. For people who have experience helping nervous rescue cats settle indoors. Can providing a dedicated enclosed hiding space genuinely improve their confidence and reduce stress during the first few months after adoption?