feat(lanes): auto-advance a codex lane's stage from its rollout detection

A codex session emits no hooks and rarely calls `ccam stage` on its own, so
its card sat at `idle` forever while the amber "detected" badge was the only
thing that ever moved. `codex-ingest.js` now advances the declared `stage`
from its own written detection — the one place in CCAM where an inference
moves the blue `current` ring, and only for `codex` lanes.

It stays honest: gated on `recordDetection` having written (so forward-only,
declared-wins and the detection TTL are inherited unchanged), passes NO
evidence (the node renders `passed-no-evidence` amber, never `done`), and no
template's last node carries detect rules, so a lane can never be
auto-declared `done`. `setStage` grows a `keepDetection` option — its sole
caller — so the detection columns survive the advance and the card keeps
showing which command moved it instead of looking like an agent's own claim.

Two levers then get the evidence auto-advance cannot supply:

- `codex-nudge.js` now nudges on a stage held 2+ min with no evidence,
  instead of on a detection sitting ahead of the declared stage — after
  auto-advance the old condition can never fire, since the two now match.
- `ccam lanes agents install` on a codex lane writes the marker-delimited
  `<!-- ccam:stage:start -->` block into the lane's own AGENTS.md — the one
  instruction channel Codex reads — instead of copying agent templates into
  `.claude/agents/`, which it never loads. Appended, user prose preserved,
  reinstall replaces exactly that block.

Verified with a real `codex exec` run: stage moved to `watching-pr` with
`evidence: null` and the detection signal intact. 1364 server tests pass.

server/__tests__/lane-agents.test.js

@@ -115,4 +115,30 @@ describe("installAgents", () => {
     await installAgents(lane);
     assert.ok(fs.existsSync(path.join(cwd, ".claude", "agents")));
   });
+
+  it("installs the AGENTS.md stage block for a codex lane, not .claude/agents/", async () => {
+    const cwd = makeRepoDir();
+    const lane = lanesLib.createLane({ title: "cx", cwd, kind: "managed", tool: "codex" });
+
+    const result = await installAgents(lane);
+    assert.deepEqual(result.installed, ["AGENTS.md"]);
+    assert.equal(fs.existsSync(path.join(cwd, ".claude", "agents")), false);
+    const doc = fs.readFileSync(path.join(cwd, "AGENTS.md"), "utf8");
+    assert.match(doc, /ccam stage <stage> --tool codex/);
+  });
+
+  it("preserves the user's own AGENTS.md prose and replaces only the block", async () => {
+    const cwd = makeRepoDir();
+    const lane = lanesLib.createLane({ title: "cx", cwd, kind: "managed", tool: "codex" });
+    const file = path.join(cwd, "AGENTS.md");
+    fs.writeFileSync(file, "# House rules\n\nNever force-push.\n");
+
+    await installAgents(lane);
+    await installAgents(lane); // reinstall must not duplicate the block
+
+    const doc = fs.readFileSync(file, "utf8");
+    assert.match(doc, /Never force-push\./);
+    assert.equal(doc.split("<!-- ccam:stage:start -->").length - 1, 1);
+    assert.equal(doc.split("<!-- ccam:stage:end -->").length - 1, 1);
+  });
 });