Tbh I prefer the visual novel over the manga. They have made slight modifications in the manga adaptation and went overboard with the action imo. I know this is Annie but beating up multiple groups of people scene after scene felt lto me ike her fighter part was over done. I have read two chapters of the manga and completed the VN and I will be judging this based on the VN (For reasons memtioned above). I don't know whether this is cannon or not, but the relationship between Annie and her father is explained in a really amazing manner and this part of the side story allows a person to get a much better view and understanding of Annie's character, if they didn't before. I really liked this part of the story and the ending as well where it is more than clear why Annie has to go about this course of action, and also chooses to carry it out.
The only cons I see in this is Annie's depiction of being a detective/ playing detective for the time being. I felt that was simply out of her character and she definitely isn't the type of person to walk up to a noble's mansion and comply to sit there and listen to him. As for the canon part, I don't see this being canon either but I am sure the depiction of the relationship between Annie and her father was more then accurate. I cannot see any other way this could have gone about.
Edit:
OMG, I read the third chapter that Eigengrau linked and this thing is over-exaggerated! Also deviates a lot. In the VN Annie makes it to the office where Carly is held and finds a group of people drinking on the first floor. It is night and she hides in the shadow of the nearby building waiting for them to get drunk. Once drunk she enters and confronts the 5 men who she incapacitates to save Carly. The VN states the presence of 5 men and no more.
Another huge difference that the VN had was that Annie was shot in the stomach, contrary to what happens in the manga where she was shot in the heart. Along with that, the VN clearly states the bullet leaving her body and lodging itself into the wall behind her, after the shooting. Besides, the scenes in the carriage is slightly different too, but the carriage deviations barely change anything within the plot and can be looked over. All in all again, I feel that the VN gave out a much better image of whatever had to transpire in the side story, and was spot on in delivering the relationship between Annie and her dad. I may post the link to the VN later when I come across it. It is worth reading, be it canon or not.