[FEATURE] One-click session handoff: end a session into a new linked one, shown as a thread in the session list

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet (related but different: #11455 asks for generic continuity/cross-machine handoff, #74141 asks for manual folders/groups in the recents list — this request is about continuation as a first-class action that produces the grouping automatically)
• [x] This is a single feature request (not multiple features)

Problem Statement

With prompt caching, session cost is roughly context size × turns — for my usage ~96% of spend is cache reads. The cheapest way to work is therefore many short sessions instead of one long one: end a session at a task boundary and continue in a fresh, small-context session.

Claude Code has no native support for this pattern, so it's all manual:

1. Ending a session means asking the model to write a "handoff prompt" (goal, next step, links), copy-pasting it into a new session, and hoping the model included a pointer back to the source transcript.
2. The session list then fills with lookalike entries ("regression testing status", "regression testing status", "regression next steps"…) with no indication they're one piece of work. After a meeting or a day away, reconstructing which of 10 sessions is the live tip of which piece of work is real overhead.

Proposed Solution

• A "Continue in new session" action (Desktop button and/or CLI command): the model writes a handoff summary, the current session ends, and a new session starts seeded with that summary — like /compact, but into a fresh session, keeping the small-context cost benefit.
• The new session is linked to its predecessor as a thread: the session list renders the chain grouped/ordered (or collapsible to the latest tip), so a multi-session piece of work reads as one story. Archive-the-thread becomes one action when the work ships.
• The linked successor can read its predecessor's transcript on demand (the transcript-search tools already exist), so the handoff summary doesn't have to carry everything.

Alternative Solutions

Currently emulated with: a skill that writes handoff prompts including the source session's title, search_session_transcripts in the successor to reach back, a strict title convention (<clone>: <thread> — <topic>) applied via set_session_title, and spawn_task chips to make the handoff one click. It works, but it's a stack of conventions doing what one primitive could.

Priority

High - Significant impact on productivity

Feature Category

Other (Desktop app session management)

Use Case Example

1. I'm running an iOS release across a day: kickoff → regression testing → bug triage → release tickets. Each phase is a natural session boundary.
2. At each boundary I click "Continue in new session"; the handoff carries the 3-line state and the ticket links.
3. Coming back after meetings, the session list shows one thread ("10.35.0 release", 6 sessions, tip: "release tickets") instead of six unrelated-looking entries.
4. When the release ships, I archive the thread in one action.