[gaord]

Refs #6483 — the saved-history alignment this fork cut rebases onto. The endpoint has no tracking issue of its own; the client half lands separately in the CodeWhale VSCode extension.

Adds one endpoint:

• POST /v1/threads/{id}/fork-at-turn ({"turn_id": "turn_…"}) forks a thread at a named user turn. The fork keeps that turn and every turn before it and drops the turns after it; naming the last turn therefore keeps the whole conversation. The receipt is /undo's shape (thread, original_user_text, original_user_images) and carries the first dropped turn's prompt — what was asked next — so a client can put it back in the composer.

Why a named turn instead of another depth: a client cannot count these turns for itself. The transcript a client renders and the turn store this cuts are not the same list — steers, image-only prompts and injected handoffs each sit on one side only — so a depth the client computed is an off-by-one waiting to fork the wrong prefix while answering 201. Naming the turn moves that decision to the side that owns the list. The enumeration itself (user_turn_indices) is now one function shared by both cuts.

No file rollback: the branch left behind shares the workspace, so a fork stays a sibling conversation and only /undo and /patch-undo touch files. The suffix-cloning path is shared with the depth-relative cut (prepare_fork_from_cutoff), which is where the two anchors could otherwise drift apart in the saved-history alignment added by #6483 — that alignment names the first dropped turn for either cut.

Branching is also allowed while a turn is running, and does not interrupt it (the runtime owns the turn; a client that switches away only stops watching). Nothing here reads or writes the running turn, and the new test pins that the source record, the running turn's status and its items are untouched.

Tests (all on top of main @ 8a835d7):

• cargo test -p codewhale-tui --lib fork_ → 31 passed / 0 failed (includes the two new endpoint tests: keep-the-anchor cut and returned prompt; whole-conversation cut with nothing to return; non-user turn → 400)
• cargo test -p codewhale-tui --lib undo → 19 passed; --lib retry → 74 passed; --lib saved_history → 2 passed; --lib boundary → 71 passed
• rustfmt --edition 2024 --check clean on the four touched files

End to end against a runtime built from this branch (isolated CODEWHALE_HOME, seeded from a real store, no model calls): GET-probe of the route answers 405 (what a client's capability probe needs); fork at an earlier turn keeps ["first"] and returns the next prompt; fork at the last turn keeps both turns and returns nothing; the source thread is unchanged; a non-user turn is 400 and an unknown thread is 404.

The client half (a per-turn "branch" row in the CodeWhale VSCode extension) lands separately; it is capability-gated on this route, so an older engine simply offers no row.