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.

server/routes/run.js

@@ -290,12 +290,13 @@ router.get("/binary", (req, res) => {
   // taken from a fixed allowlist, never from the query string directly — this
   // string reaches `which`.
   const tool = req.query.tool === undefined ? "claude" : String(req.query.tool);
-  if (tool !== "claude" && tool !== "codex") {
+  const bins = { claude: "claude", codex: "codex", antigravity: "agy" };
+  if (!Object.hasOwn(bins, tool)) {
     return res.status(400).json({ error: { code: "EBADTOOL", message: "unknown tool" } });
   }
   const which = require("node:child_process").spawnSync(
     process.platform === "win32" ? "where" : "which",
-    [tool],
+    [bins[tool]],
     { encoding: "utf8" }
   );
   const stdout = (which.stdout || "").trim();