Ability to Continue Composer/Chat instances in other Workspaces

It happens that I start talking to the Composer or Chat to just ask what it thinks of something from where the basic idea and structure of a folder gets based on.
While doing this I have not opened/created a workspace and upon creation of a workspace and opening it I get a new clean instance for chat and composer.
It would be great to have a way to just move the already existing session I have with chat/composer to a new workspace and be able to continue it inside it without having to reiterate on everything again as needed for a new session.

I don’t exactly know how the composer/chat integration works but it would be an amazing and helpful feature (at least from my point of view) and might maybe not even too complicated to achieve.

Thanks for considering this suggestion!
Daniel