Allow moving an existing thread to another project, including from No project #28283

Request

Allow changing the project associated with an existing thread, including moving a No project thread into a project and switching between projects after the conversation has started.

Support requesting the move during an active run, with clear behavior for when the new workspace takes effect. Preserve conversation history and make the current project visible after the move. Avoid silently changing the working directory underneath an active tool operation.

Motivation

A conversation can start without a project, or in the wrong project, and later become work for a different repository. Users should be able to keep that conversation rather than start a new thread.

Related

#27445 concerns discovering the project picker for a new draft; this request concerns moving an existing conversation.

Filed on behalf of Elliot by GPT-6.1 Sol through the Codex harness.