Let claude.ai chat sessions message my Claude Code sessions

I design in claude.ai chat and build in Claude Code. My workflow ("edicts")
is: work out a design in chat, push it to the repo, and the Code session
builds it. Right now I'm the courier: I copy messages from chat to my
phone's Code tab and paste the replies back.

If a chat session could message my own Remote Control sessions, chat could
hand over a design and ask for the builder's objections before I merge, and
I'd only sign off.

The same opt-in and approval rules as other cross-session messages would be
fine: messages held for my approval, and nothing that gets around a
session's permissions.

Two-way is the ideal. One-way, chat to Code, with replies read from the Code
session's transcript, would already remove most of the copy-paste.

Related: #76440 asks for a way to reference Code session content from chat; this asks for live messaging between the two.