Warning! Spoilers for The Haunting of Bly Manor below.
In The Haunting of Bly Manor, the dolls in Flora's dollhouse serve a secret purpose, and are moved around mysteriously. When Dani finds them scattered about, she assumes it's because Flora carelessly forgets to pick up her toys. However, the dolls represent the changing locations of the ghosts that fill the home. Flora isn't the one who moves the dolls, though, so who is?
Bly Manor follows Dani as takes on the job of governess to two orphaned children, Miles and Flora. Dani quickly realizes that something is off with the house — it's full of ghosts. Some ghosts are vengeful and out for blood. Others are simply stuck within the walls of the manor. One such ghost acts as a guardian angel for Flora.
Years prior to the events of the show, Flora sees the ghost of a young boy playing with her dollhouse, which happens to be an exact replica of her home. The two become friendly acquaintances. Throughout the rest of the show, various dolls are strategically moved around. That's because the young boy is warning Flora where everyone is — particularly the menacing lady in the lake.
Throughout the show, Flora pays close attention to the location of the dolls around her house — whether it be in the dollhouse or her actual home. Flora has dolls to represent everyone, living or dead, who lives in Bly Manor. The audience comes to realize that the dolls' locations represent that person or ghost's location in the house or on the grounds. Since he was shown playing with the dollhouse and can regularly interact with the ghosts at Bly Manor, it's meant to be understood that the doll-face ghost is the one who scatters Flora's dolls about.
During their first meeting, Flora was kind to the doll-face ghost, so this is his way of returning the favor. The lady in the lake cursed Bly Manor's dead to remain there as ghosts. In turn, every ghost fears her. While it's beneficial for Flora to know where everyone is in the house, it's absolutely crucial to know where the lady in the lake is. When he places her under Flora's dresser, she's asleep in the lake. When she's inside the dollhouse, she's in the actual house.
Family, both blood and chosen, is an important element in The Haunting of Bly Manor. The doll-face ghost was just a young boy at the time of his death. He still yearns for that attachment, and Flora gives that to him. By warning her of the lady in the lake's location, the doll-face ghost allows Flora to protect the people in her life — particularly Dani. That bond is what prompts Dani to sacrifice herself in The Haunting of Bly Manor's ending. But it all started with the simple act of kindness and good-intentioned warnings from the doll-face ghost.