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.

client/src/lib/types.ts

@@ -2410,7 +2410,14 @@ export interface ProofFeature {
 }
 
 /** Which CLI drives a lane's pane. Fixed at lane creation and never patched. */
-export type LaneTool = "claude" | "codex";
+export type LaneTool = "claude" | "codex" | "antigravity";
+
+/** How each CLI is named on screen (strip tag, console title, prompt box). */
+export const LANE_TOOL_LABEL: Record<LaneTool, string> = {
+  claude: "Claude",
+  codex: "Codex",
+  antigravity: "Antigravity",
+};
 
 export interface Lane {
   id: number;