fix(run): plumb the recorded prompt back into live runs, fix lane routing when the cwd doesn't match the selected lane

- pty-run.js's publicRun() now reads promptPreview back from the
  dashboard_runs row it already wrote at spawn time (was persisted,
  never read back) — RunHandle carries it through to the client.
- Workspace.tsx's onStartFromSetup no longer trusts RunSetup's
  always-populated laneId prop to decide whether a new lane needs
  ensuring — it re-resolves the target lane from the cwd the user
  actually typed, so starting a run with a different cwd than the
  currently-selected lane correctly ensures/creates the right lane
  instead of silently starting in the wrong one.

Fixes findings from the Task 8+9+10 review that a prior fix attempt
left unresolved (2f39f4e's --no-verify commit, and an incomplete
diagnosis of the lane-routing bug as a test-harness artifact).

client/src/pages/Workspace.tsx

@@ -50,6 +50,7 @@ import type {
   RunHandle,
   RunListResponse,
   RunMode,
+  RunStartArgs,
 } from "../lib/api";
 import type {
   Session,
@@ -606,7 +607,7 @@ export function Workspace() {
   }, [binaryStatus, prompt, cwd, busy, handle, start]);
 
   const onStartFromSetup = useCallback(
-    async (args: any) => {
+    async (args: RunStartArgs) => {
       if (busy) return;
       setBusy("start");
       setError(null);
@@ -621,29 +622,30 @@ export function Workspace() {
           throw new Error(t("errors.cwdRequired"));
         }
 
-        let targetLaneId = args.laneId;
-        if (!targetLaneId) {
-          // If no lane provided, try to find or create one
-          const ownedLane = lanes.find((l) => l.cwd === effectiveCwd);
-          if (ownedLane) {
-            targetLaneId = ownedLane.id;
-            setSelectedLaneId(ownedLane.id);
-          } else {
-            try {
-              const ensureResult = await api.lanes.ensure({ cwd: effectiveCwd });
-              targetLaneId = ensureResult.lane.id;
-              setSelectedLaneId(ensureResult.lane.id);
-              setLanes((prev) => {
-                const exists = prev.some((l) => l.id === ensureResult.lane.id);
-                return exists ? prev : [...prev, ensureResult.lane];
-              });
-            } catch (err) {
-              throw new Error(
-                t("errors.laneCreateFailed", {
-                  message: err instanceof Error ? err.message : "unknown",
-                })
-              );
-            }
+        // Resolve the lane from the cwd the user actually typed, not from
+        // args.laneId — RunSetup always supplies the currently-selected lane's id
+        // (a required prop), which would otherwise silently start a run in the wrong
+        // lane whenever the user types a cwd different from the one currently selected.
+        const ownedLane = lanes.find((l) => l.cwd === effectiveCwd);
+        let targetLaneId: number;
+        if (ownedLane) {
+          targetLaneId = ownedLane.id;
+          if (ownedLane.id !== args.laneId) setSelectedLaneId(ownedLane.id);
+        } else {
+          try {
+            const ensureResult = await api.lanes.ensure({ cwd: effectiveCwd });
+            targetLaneId = ensureResult.lane.id;
+            setSelectedLaneId(ensureResult.lane.id);
+            setLanes((prev) => {
+              const exists = prev.some((l) => l.id === ensureResult.lane.id);
+              return exists ? prev : [...prev, ensureResult.lane];
+            });
+          } catch (err) {
+            throw new Error(
+              t("errors.laneCreateFailed", {
+                message: err instanceof Error ? err.message : "unknown",
+              })
+            );
           }
         }