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/README.md

@@ -555,7 +555,12 @@ failures return `500` with `error.stderr`.
 
 `start` returns `409 ERUNLIVE` when the lane's recorded run is still `spawning`
 or `running`: overwriting `run_id` would orphan that child, and a later `reset`
-would then `git clean -fd` a directory the orphan is still writing into.
+would then `git clean -fd` a directory the orphan is still writing into. It
+returns the same code when the lane's tmux pane is running an agent and the
+request carried a `prompt` or `resumeSessionId` — `pty-run.js` will not type
+over a live agent, and adopting the pane silently would answer 200 for a resume
+that never spawned. `POST /api/run` maps that code to `409` too; a start with
+neither field still adopts the pane.
 
 Besides the stage a skill declares explicitly, every lane also carries a
 server-inferred `detected_stage`: `server/lib/stage-detect.js` matches each