Feature request: ability to migrate/transfer a Claude Code session to claude.ai browser chat

Claude Code sessions often start with a hands-on technical task (file editing, terminal diagnostics, etc.) but naturally evolve into broader conversations. Once the technical work is done, there's no way to hand off the conversation to claude.ai — you're either stuck in the CLI for the whole thing, or you abandon the thread and start over in the browser, losing context.

It would be useful to have a way to:

• Export/transfer a Claude Code session into the browser chat history, or
• Continue a session in claude.ai with the conversation context intact

The use case: a user needed terminal access to diagnose an audio issue (pipewire-pulse crash). Once resolved, the conversation moved into DAW recommendations, photography workflow, and personal topics — none of which needed the CLI. A smooth handoff to the browser at that point would have been the natural move.