Thank you for your question. Braces treatment combined with jaw surgery is usually indicated when the malocclusion (bad bite) is a result of malposition teeth and/or malposition jaws. You can read more about some of the common indications of jaw surgery in this article here: https://www.doctorxdentist.com/corrective-jaw-orthognathic-surgery
Braces treatment has its limitation and can only correct the position of the teeth. There have been recent advances such as the use of microimplants combined with braces treatment to try to stretch the envelope of what braces can treat. However, when the cause of the malocclusion is due to the jaw position, the ideal treatment plan will involve correcting the jaw position to get a better result facially as well as functionally. While not every patient is keen on surgery, sometimes your dentist/orthodontist may be able to camouflage the teeth position to mask the underlying jaw discrepancy. This may not be suitable for every case and would have to be determined after a careful clinical and radiographic evaluation.
Treatment time with a combined braces and jaw surgery approach is very case dependent. It would be hard to make a blanket statement on whether jaw surgery shortens treatment time. Factors such as the amount of crowding, and the treatment plan both the braces and surgical treatment plan all contribute to the overall treatment time. Based on the photos you have sent, your malocclusion seems to be mainly due to the underlying jaw malposition as the teeth are well aligned. Hence treatment time will shorten if the treatment plan is to treat the source of the problem rather than camouflage the teeth position to the jaw position.
Hope this helps and all the very best.