Best way to move a long Claude project chat into a fresh chat without losing context?

I’ve been using one Claude chat for about 2 weeks for a large project, and it’s starting to get really slow/laggy on my Windows PC in both the browser and desktop app. Weirdly, it still feels fine on my iPhone.

I don’t want to lose all the context and start over. I tried asking Claude to “print out the full context” and moving that into a new chat, but the new chat didn’t really understand the project the same way.

For people working on long projects, what’s the best way to migrate context into a fresh Claude chat? Do you use Projects, a handoff doc, summaries, pinned requirements, exported files, or something else?

Looking for an actual workflow, not just a complaint about performance.