How does axis tilt affect day length?
It does not.
The speed at which the earth rotates determines the length of the day.
Axial tilt determines the length of daylight at any point on the earth. The 23.5 degrees of tilt and the position of the north pole relative to the sun factors in. When the pole is tilted towards the sun, daylight is longer than when it is pointed away. The picture below demonstrates this.