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/lib/pty-run.js

@@ -200,7 +200,13 @@ function spawnRun(args) {
     dashboardRuns.recordRun({
       id,
       sessionId: resumeSessionId || null,
-      mode: null,
+      // `dashboard_runs.mode` is NOT NULL. Passing null made every insert throw
+      // inside recordRun's best-effort catch, so no tmux-backed run was ever
+      // persisted: publicRun then read its cwd/model/prompt/startedAt off a row
+      // that did not exist (a blank row dated Jan 1 1970 in the runs modal), and
+      // session_id never landed either, so a resumed session stayed listed as a
+      // separate `external` row. Every run here is one interactive pane.
+      mode: "interactive",
       cwd,
       tool: tool === "codex" ? "codex" : "claude",
       model: model || null,
@@ -238,6 +244,18 @@ function spawnRun(args) {
   // Pane is running something (a live `claude`, an editor, a build): adopt
   // silently, same convention as this repo's server port-adoption logic — no
   // error, no duplicate session. Attaching shows the user what is running.
+  //
+  // Adopting is only honest when the request asked for nothing more than a
+  // pane. A Resume or an initial prompt cannot be delivered into a pane that is
+  // already running an agent (typing over it is what the shell-pane branch
+  // above exists to avoid), so answering 200 there reports work that never
+  // happened: the user sees "resumed" while no `--resume` was ever spawned.
+  else if (resumeSessionId || initialPrompt) {
+    throw makeErr(
+      "ERUNLIVE",
+      `lane ${laneId}'s pane is already running \`${tmux.paneCommand(id) || "a process"}\` — stop it before resuming a session or sending a prompt`
+    );
+  }
 
   return getRun(id);
 }