Does anyone actually switch between AI models mid-conversation? And if so, what happens to your context?

I want to ask something specific that came out of my auto-routing thread earlier. A lot of people said they prefer manual model selection over automation - fair enough. But that raised a question I haven't seen discussed much: When you manually switch from say ChatGPT to Claude mid-task, what actually happens to your conversation? Do you copy-paste the context across? Start fresh and re-explain everything? Or do you just not switch at all because it's too much friction? Because here's the thing - none of the major AI providers have any incentive to solve this problem.