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.

client/src/components/run/RunHistory.tsx

@@ -521,14 +521,17 @@ function UnifiedRunRowView({
 }) {
   const { t } = useTranslation("run");
   const startedDate = new Date(row.startedAt);
-  const startedLabel = isNaN(startedDate.getTime())
-    ? "-"
-    : startedDate.toLocaleString(undefined, {
-        month: "short",
-        day: "numeric",
-        hour: "2-digit",
-        minute: "2-digit",
-      });
+  // 0 is "unknown", not the epoch — a run whose persisted row is missing has no
+  // start time, and printing "Jan 1, 08:00 AM" for it reads as real data.
+  const startedLabel =
+    !row.startedAt || isNaN(startedDate.getTime())
+      ? "-"
+      : startedDate.toLocaleString(undefined, {
+          month: "short",
+          day: "numeric",
+          hour: "2-digit",
+          minute: "2-digit",
+        });
   // Without mode distinction, offer resume for any finished run with a session.
   // An external session is live but has no attachable tmux session, so Resume
   // (a new tmux-backed `claude --resume` in its cwd) is what it gets instead.

client/src/components/run/__tests__/RunHistory.test.tsx

@@ -242,6 +242,14 @@ describe("ActiveRunsSwitcher", () => {
     expect(screen.queryByText(i18n.t("run:runs.externalBadge"))).toBeNull();
   });
 
+  it("shows a dash, not the epoch, for a row with no start time", () => {
+    // A run whose persisted row is missing arrives with startedAt 0. Rendering
+    // that as "Jan 1, 08:00 AM" presents a gap in the data as real data.
+    renderModal([row("no-start", { startedAt: 0 })]);
+    expect(screen.getByText("-")).toBeTruthy();
+    expect(screen.queryByText(/Jan 1,/)).toBeNull();
+  });
+
   it("fires attach with the run id of the row that was clicked", () => {
     const { spies } = renderSwitcher();
     openModal();