You can’t add a NOT NULL column to a table that has more than zero rows, when the column is constrained to values that match those in the parent table, and yet has only NULL values because it’s a new, unpopulated column with no DEFAULT.
The workaround is to do it in stages: add the column, but don’t declare it NOT NULL, and don’t declare the foreign key yet.
ALTER TABLE boys
ADD COLUMN toy_id INT;
Then populate it with valid data that matches some value(s) in your toys table.
UPDATE boys SET toy_id = ...;
Then alter the column to be NOT NULL, and create the constraint:
ALTER TABLE boys MODIFY COLUMN toy_id INT NOT NULL,
ADD CONSTRAINT toys_toy_id_fk
FOREIGN KEY(toy_id)
REFERENCES toys(toy_id);