Should the entire set be changed at the same time?
In principle, yes. When changing a single string, the instrument sounds better in the short term, and usually brighter. The new “young” string provides many overtones and also passes these on to strings located next to it. Since the “old” neighboring strings no longer produce enough overtones, the new, young string becomes more rapidly overburdened in the production of overtones and very quickly loses its brilliance as a result. The exception to this is the unwound violin E-string. It can be changed at any time as it barely affects the life span of the other strings. The A-string also becomes fresher if a new E-string is fitted since the new E provides brightness to the A.