[Feature Request] Let a Claude Design session talk directly to its paired Claude Code session — right now the handoff is manual

Problem

Claude Design and Claude Code are two separate conversational surfaces with no live connection between them. The only bridge today is /design-sync (the claude_design MCP / DesignSync tool), which is a one-directional, file-level batch operation: list files, build a plan, get it approved, push or pull a set of files. That's useful for syncing a component library, but it isn't communication — there's no way for something decided or asked mid-conversation in a Design session to reach the paired Code session (or vice versa) without the user manually copying it across themselves.

In practice this means going back and forth between two separate chat windows by hand — reading a decision in one, retyping or pasting it into the other, then doing the same in reverse when the other side needs to ask a follow-up question. For any real back-and-forth (not just "here's a finished component, sync it over"), this gets painful fast, and it's pure manual relay work that adds nothing — the user is acting as the message bus between two agents that are both fully capable of just talking to each other.

Proposed solution

Let a Design session and its paired Code session exchange messages directly — even a minimal version would help: either session can post a message/question into the other's context (with the user seeing and able to interrupt/redirect either side), instead of requiring the user to manually relay every exchange. This is a live communication channel, not a file-sync artifact — it doesn't need to solve schema drift or contract versioning to be useful; it just needs to remove the user from the middle of a conversation that's happening between two Claude sessions anyway.

Related, but not a duplicate

#70040 ("Design Contract — a continuity bridge between Claude Design and Claude Code") proposes a much heavier mechanism — a versioned, git-tracked contract file capturing component states, data bindings, and backend dependencies, aimed specifically at UI/backend drift detection. That's a good idea for a different problem (structured artifact continuity across cold starts). This request is smaller and more general: just let the two sessions talk, for the ordinary case of "the two of you sort this out between yourselves" instead of the user manually carrying every message across.