feat(lanes): Antigravity lanes, release exited panes, fresh Codex starts

- antigravity: a third lane tool running Antigravity's `agy` CLI. `-i`
  carries the first prompt, `--continue` resumes; `agy` has no model,
  effort or permission flag, and `--dangerously-skip-permissions` is never
  emitted. No pipeline, no agents install, and no AI Router (native only,
  else EUNSUPPORTED). Add lane gains an Antigravity choice and the binary
  probe maps it to `agy`.
- UI: the lane card no longer renders a frame holding only a "Codex" chip,
  and the prompt box names the lane's CLI ("Ask Codex anything…"), via
  LANE_TOOL_LABEL.
- runs: a pane that exits is released on a 10 s server beat
  (healAllRunIds, DASHBOARD_RUN_HEAL_MS). Codex and Antigravity fire no
  hook, so their lanes stayed "running" until something re-read them.
- codex: Start no longer sends resumeLast — only "Resume last session"
  continues the previous thread.

docs/API.md

@@ -2061,7 +2061,7 @@ The `/api/run/*` namespace starts and manages `claude` subprocesses in tmux-back
 ```http
 GET    /api/run                       List all live runs (computed fresh from tmux state)
 GET    /api/run/tmux                  { available: bool } — whether tmux is on PATH
-GET    /api/run/binary?tool=          { found, path } for the `claude` or `codex` binary
+GET    /api/run/binary?tool=          { found, path } for the `claude`, `codex` or `agy` binary
 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
@@ -2074,7 +2074,7 @@ DELETE /api/run/:id                   Kill (SIGTERM → SIGKILL after 5 s)
 
 `:id` must be a lane pane name, `agenthub-lane-<n>`; anything else answers 404 without reaching tmux, so these two routes can never touch a tmux session the dashboard did not start.
 
-**`GET /api/run/binary`:** Probes for the binary (`claude` or `codex`). Optional query parameter `?tool=codex` probes for Codex; omitted or `?tool=claude` probes for Claude. Returns `{ found: bool, path: string | null }`.
+**`GET /api/run/binary`:** Probes for the binary (`claude`, `codex` or `agy`). Optional query parameter `?tool=codex` probes for Codex and `?tool=antigravity` for Antigravity's `agy`; omitted or `?tool=claude` probes for Claude. Returns `{ found: bool, path: string | null }`.
 
 **`POST /api/run` (start/attach):** Requires `laneId` (the lane this run belongs to). Creates or attaches an existing tmux session named `agenthub-lane-<id>` in the lane's working directory. If that session already exists and its pane is idling at a shell prompt, the appropriate command line (including `--resume` and any initial prompt) is typed into that pane instead of being dropped; if the pane is running a program, the request adopts the session unchanged. 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.