I can't really answer that question about what happens between the 3- and 6-month mark. We don't really know why an extended period of keto-dieting causes the senescence response. But the interindividual differences are relative large. That is everybody reacts differently, and the 3-month period is not a given for everybody.
Your suggestion that there is an increase in desire for carbs, is an interesting one. From my personal experience I would subscribe to that idea. And from what I learned from trial participants and clients, your suspicion may have some base.