The heart can cause shortness of breath as well. For example, inefficient pumping (eg fluid in pericardium or damaged heart muscle) = not enough oxygen transport, and thus SOB.
In this instance, the person has both heart and lung issues - it is up to the doctors to determine which is causing the specific symptoms. It could be the congestive heart failure, or the bronchiectasis, or the infection, or a combination of all three.