It depends on where the egress doorway is located.
If the door is located directly ahead from the last step, then the 44 inches is measured from the last riser to the door. However, per ANSI A117.1, you need 48 inches of depth for maneuvering clearance for a forward approach on push side, so the depth of the landing will require 48 inches. Plus, since the door will have a closer and a latch, you need 12 inches of clearance on the latch side. This would place the handrail extension inside of the maneuvering clearance, so the 48-inch-deep clearance would be measured from the end of the handrail extension.
The door can be placed on the same wall, but inline with the other side of the stair, making for a side approach on the push side of the door. Since the door has a closer and latch, the width of the maneuvering clearance is also required to be 48 inches, so the handrail extension would have to be outside of that clearance.
If the door is on the wall facing the open side of the stair, that would allow a forward approach, too. At 48 inches in depth, this would probably clear the handrail extension since the width of the enclosure is 96 inches. The landing can be the 44 inches measured from the last riser, which would provide the minimum accessible width of 32 inches clear (44 inches minus 12 inches of handrail extension), but would not provide the minimum width of 44 inches for means of egress (39-1/2 inches of clear width with 4-1/2 inches of permitted handrail extension into the required egress width). Thus, the depth of the landing would need to be 51-1/2 inches.
The door can be on the wall on the stair side of the enclosure, but the landing would need to provide for the width of the door plus 24 or 22 inches, depending on which side of the door the latch is located. It would also require 48 inches of width because of the closer and latch, which may cause the handrail extension on the open side to encroach into the maneuvering clearance.