fix(runs): persist tmux-backed runs so a resumed session shows its own info

`dashboard_runs.mode` is NOT NULL and `recordRun` swallows insert errors by
design, so pty-run.js passing `mode: null` meant NO tmux-backed run was ever
persisted — the newest row in a live database dated from before pty-run.js
replaced run-spawner.js. `publicRun` reads cwd, model, prompt preview,
started_at and session_id off that row and the handle itself is recomputed
from tmux, so the runs modal rendered a live row with no cwd, no model, no
prompt and a start date of Jan 1 1970. The same missing row is why a resumed
session kept its separate `external` badge: the client dedupes an external
session against the session ids carried by run rows, and no run row ever
carried one.

- pty-run.js records `mode: "interactive"` — every run here is one pane.
- dashboard-runs.js still never fails a live run on a db error, but warns
  instead of swallowing silently; that silence hid this for six weeks.
- RunHistory renders `startedAt: 0` as "-" rather than dating a row with no
  known start time to the epoch.

Also closes the other half of the same lie: adopting a pane that is already
running an agent now throws ERUNLIVE (409 from both the lane start action and
POST /api/run) when the request carried a prompt or a resumeSessionId. That
argv cannot be typed over a live agent, so answering 200 reported a resume
that never spawned. A start asking for nothing but a pane still adopts.

server/__tests__/pty-run.test.js

@@ -335,4 +335,91 @@ describe("pty-run", () => {
     );
     assert.ok(!call.some((a) => String(a).startsWith("--dangerously-bypass")));
   });
+
+  // `dashboard_runs.mode` is NOT NULL and recordRun swallows insert errors, so a
+  // null there persisted nothing at all while every call still looked fine: the
+  // runs modal rendered a row with no cwd, model, prompt or start time, and a
+  // resumed session kept its separate `external` row because no run row ever
+  // carried its session id. These assert the row actually lands.
+  it("refuses to swallow a resume or a prompt when the pane already runs an agent", () => {
+    // Adopting silently here answered 200 while spawning no `--resume` at all:
+    // the dashboard reported a resumed session that never happened.
+    tmux.__setExecImpl((args) => {
+      if (args[0] === "display-message") return "claude\n";
+      return ""; // has-session succeeds → pane is busy with a live agent
+    });
+    assert.throws(
+      () => pty.spawnRun({ laneId: 51, cwd: "/tmp/repo", resumeSessionId: "abc12345" }),
+      (err) => err.code === "ERUNLIVE"
+    );
+    assert.throws(
+      () => pty.spawnRun({ laneId: 51, cwd: "/tmp/repo", initialPrompt: "do the thing" }),
+      (err) => err.code === "ERUNLIVE"
+    );
+  });
+
+  it("still adopts a busy pane when the request asked for nothing but a pane", () => {
+    const calls = [];
+    tmux.__setExecImpl((args) => {
+      calls.push(args);
+      if (args[0] === "display-message") return "claude\n";
+      return "";
+    });
+    const handle = pty.spawnRun({ laneId: 52, cwd: "/tmp/repo" });
+    assert.equal(handle.id, "agenthub-lane-52");
+    assert.ok(!calls.some((c) => c[0] === "new-session"));
+    assert.ok(!calls.some((c) => c[0] === "send-keys"));
+  });
+
+  describe("run persistence", () => {
+    const dashboardRuns = require("../lib/dashboard-runs");
+
+    it("spawnRun persists the run so the runs list has cwd, model and prompt", () => {
+      tmux.__setExecImpl((args) => {
+        if (args[0] === "has-session") {
+          const e = new Error("gone");
+          e.status = 1;
+          throw e;
+        }
+        return "";
+      });
+      pty.spawnRun({
+        laneId: 71,
+        cwd: "/tmp/persisted",
+        model: "claude-opus-5",
+        initialPrompt: "ship it",
+      });
+
+      const row = dashboardRuns.getRun("agenthub-lane-71");
+      assert.ok(row, "expected a dashboard_runs row for the spawned run");
+      assert.equal(row.cwd, "/tmp/persisted");
+      assert.equal(row.model, "claude-opus-5");
+      assert.equal(row.prompt_preview, "ship it");
+      assert.equal(row.lane_id, 71);
+      assert.ok(row.started_at, "started_at must be set, or the UI dates the row to the epoch");
+      assert.ok(row.mode, "mode is NOT NULL — a null here silently drops the whole insert");
+    });
+
+    it("a resumed run carries the session id, which is what dedupes the external row", () => {
+      tmux.__setExecImpl((args) => {
+        if (args[0] === "has-session") {
+          const e = new Error("gone");
+          e.status = 1;
+          throw e;
+        }
+        return "";
+      });
+      const sessionId = "c2055094-09cf-4735-9712-09e5cdf7023f";
+      const handle = pty.spawnRun({
+        laneId: 72,
+        cwd: "/tmp/resumed",
+        resumeSessionId: sessionId,
+      });
+
+      // The UI reads sessionId off the run list; an external session whose id is
+      // already on a run row is not repeated as its own `external` row.
+      assert.equal(handle.sessionId, sessionId);
+      assert.equal(dashboardRuns.getRun("agenthub-lane-72").resume_session_id, sessionId);
+    });
+  });
 });