[Feature]: Rehome an existing thread to another project

[LunarRed]

Problem

I sometimes start a substantial fix under the wrong T3 Code project. Once the conversation has accumulated useful investigation, decisions, and context, there is no way to move it to the correct project. The current workaround is to start a new thread and manually summarize or copy the previous conversation.

Desired behavior

From a thread's context menu, select:

Move to project… → <target project>

The thread should then:

• appear under the target project
• preserve its title and conversation history
• use the target project's workspace for future turns
• continue working without requiring manual conversation transfer

Proposed initial scope

• projects within the same T3 environment only
• idle threads only
• no cross-server transfer
• clear confirmation showing the source and target workspace paths
• filesystem changes are not automatically copied between unrelated repositories

Open implementation questions

A project determines the agent working directory, so this is more than a sidebar metadata change:

• Should the existing provider session be resumed in the new directory, or should T3 Code start a fresh provider session using the preserved history?
• Should checkpoint history be reset when the projects use different Git repositories?
• What should happen to an associated worktree, branch, terminals, and pending approvals?
• Should moving be restricted when the source contains uncommitted changes?

My preference is to preserve the visible T3 conversation while safely starting future work in the target project's workspace, even if that requires resetting provider/checkpoint state.

I’m willing to implement this after the desired semantics are confirmed.