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/routes/lanes.js

@@ -898,7 +898,9 @@ function sendLifecycleError(res, err) {
   if (["ENOTMANAGED", "EOUTSIDEROOT", "ENOTWORKTREE", "EEXPECT"].includes(err.code)) {
     return res.status(400).json({ error: { code: err.code, message: err.message } });
   }
-  if (["ESTALE", "EUNPUSHED"].includes(err.code)) {
+  // ERUNLIVE: the lane's pane is busy with a live agent, so a resume/prompt
+  // could not be delivered — a conflict, not a bad request or a server fault.
+  if (["ESTALE", "EUNPUSHED", "ERUNLIVE"].includes(err.code)) {
     return res.status(409).json({
       error: {
         code: err.code,

server/routes/run.js

@@ -256,6 +256,10 @@ router.post("/", (req, res) => {
     });
     return res.status(201).json(handle);
   } catch (err) {
+    // A busy pane is a conflict with live state, not a malformed request.
+    if (err.code === "ERUNLIVE") {
+      return res.status(409).json({ error: { code: err.code, message: err.message } });
+    }
     if (err.code && err.code.startsWith("E")) {
       return res.status(400).json({ error: { code: err.code, message: err.message } });
     }