docs: fix Task 12 Round 1 accuracy findings

- Fix POST /api/run param: change 'prompt' to 'initialPrompt' (Finding 1)
- Fix POST /api/run response shape: show actual fields from publicRun() (Finding 2)
- Delete stale 'Running and releasing lanes' section with old POST /api/lanes/:id/start (Finding 3)
- Delete stale POST /api/lanes/:id/message section — endpoint now returns 400 EUNSUPPORTED (Finding 4)

All changes verified against actual code:
- server/routes/run.js:285 uses body.initialPrompt
- server/lib/pty-run.js:144-156 publicRun() returns {id, laneId, status, cwd, model, ...}
- server/routes/lanes.js:1134 message action returns 400 error

docs/API.md

@@ -1480,12 +1480,12 @@ GET    /api/run/cwds                  Suggested cwds (dashboard, home, recent)
 GET    /api/run/history?limit=&laneId=  Persisted run history; laneId narrows to one lane's runs
 GET    /api/run/files?cwd=&q=         Fuzzy file search inside cwd for the @-file autocomplete
                                        (skips node_modules, .git, dist, build, .next, .cache, coverage, vendor)
-POST   /api/run                       Start/attach run — Body: { laneId, prompt?, ... }
+POST   /api/run                       Start/attach run — Body: { laneId, initialPrompt?, ... }
 GET    /api/run/:id                   Run handle (returns live run state)
 DELETE /api/run/:id                   Kill (SIGTERM → SIGKILL after 5 s)
 ```
 
-**`POST /api/run` (start/attach):** Requires `laneId` (the lane this run belongs to). Creates or attaches an existing tmux session named `ccam-lane-<id>` in the lane's working directory. Optionally accepts `prompt` to immediately type/send into the session (if empty or omitted, the session is created/attached with no initial input). Returns `{ runId, tmuxSessionName, cwd, ... }`. The dashboard self-heals a lane's `run_id`/`status` on every read if the tmux session has been killed externally.
+**`POST /api/run` (start/attach):** Requires `laneId` (the lane this run belongs to). Creates or attaches an existing tmux session named `ccam-lane-<id>` in the lane's working directory. Optionally accepts `initialPrompt` to immediately type/send into the session (if empty or omitted, the session is created/attached with no initial input). Returns `{ id, laneId, status, cwd, model, permissionMode, effort, resumeSessionId, sessionId, startedAt, promptPreview }` where `id` is the tmux session name. The dashboard self-heals a lane's `run_id`/`status` on every read if the tmux session has been killed externally.
 
 **PTY streaming:** Frames from the tmux pane are streamed to the client over `/ws-pty/:runId` as binary WebSocket frames (not JSON). The Workspace page's TerminalView component feeds these frames to xterm.js for live rendering. Simultaneously, `ccam lanes shell` can attach the same session via a real local terminal, staying in sync with the browser view.
 

docs/LANES.md

@@ -375,24 +375,6 @@ three times, and the lane list is polled and re-broadcast on every hook-driven
 tool call an agent makes. The browser fetches it per card instead, on mount and
 every 30 seconds, and a failed fetch is silent.
 
-### Running and releasing lanes
-
-The Workspace page starts runs through `POST /api/lanes/:id/start`, which accepts the same `mode` and `effort` parameters as `POST /api/run`:
-
-```bash
-curl -X POST http://localhost:4820/api/lanes/5/start \
-  -H "Content-Type: application/json" \
-  -d '{"mode": "conversation", "effort": "medium"}'
-```
-
-**A finished run releases its lane.** When a spawned Claude Code process exits (normally, non-zero, killed, or never spawned), the lane's `run_id` is cleared, its `status` returns to `idle`, and the change is broadcast as a `lane_update` WebSocket message. This prevents lanes from sitting at `running` with a dead child.
-
-Runs started through a lane are recorded with the lane's id and are history-queryable:
-
-```bash
-curl http://localhost:4820/api/run/history?laneId=5
-```
-
 ## Viewing lanes
 
 List all lanes with their current status:
@@ -940,23 +922,13 @@ Start a tmux-backed run attached to the lane. The Workspace page's "Start Run" b
 ```bash
 curl -X POST http://localhost:4820/api/run \
   -H "Content-Type: application/json" \
-  -d '{"laneId": 5, "prompt": "continue the work"}'
+  -d '{"laneId": 5, "initialPrompt": "continue the work"}'
 ```
 
-The `prompt` field is optional — if omitted, the tmux session is created/attached with no initial input, and you type into the terminal directly. Returns `{ runId, tmuxSessionName, cwd, ... }`. The same tmux session persists across attach/detach cycles, so you can switch between the browser Workspace and `ccam lanes shell` seamlessly.
+The `initialPrompt` field is optional — if omitted, the tmux session is created/attached with no initial input, and you type into the terminal directly. Returns `{ id, laneId, status, cwd, model, permissionMode, effort, resumeSessionId, sessionId, startedAt, promptPreview }` where `id` is the tmux session name. The same tmux session persists across attach/detach cycles, so you can switch between the browser Workspace and `ccam lanes shell` seamlessly.
 
 **A killed run releases the lane.** When the tmux session is terminated (from the terminal, browser stop button, or external `kill`), the lane's `run_id` is cleared, its status returns to `idle`, and the change is broadcast as `lane_update`. Runs are recorded with the lane's id and are listable via `GET /api/run/history?laneId=<n>`.
 
-### message
-
-Send input to a running session. The lane must have a live `run_id` (active session). The `needs_action` flag clears automatically when the message is delivered.
-
-```bash
-curl -X POST http://localhost:4820/api/lanes/5/message \
-  -H "Content-Type: application/json" \
-  -d '{"text": "approved, proceed"}'
-```
-
 ### stop
 
 Terminate the running session. If the lane has no live run, this is a no-op (no error).