feat(client): carry the lane tool through run fixtures

client/src/components/run/RunHistory.tsx

@@ -193,6 +193,7 @@ export function ActiveRunsSwitcher({
         started_at: s.started_at,
         ended_at: null,
         isLive: true,
+        tool: "claude",
       });
       out.push({
         id: `session:${s.id}`,

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

@@ -40,6 +40,7 @@ const LANE: Lane = {
   cwd: "/workspace/a",
   branch: null,
   kind: "adopted",
+  tool: "claude",
   source_repo: null,
   pipeline: "default",
   session_id: null,
@@ -138,6 +139,7 @@ describe("LaneConsolePane", () => {
       sessionId: null,
       startedAt: null,
       promptPreview: null,
+      tool: "claude" as const,
     });
     const props = {
       ...baseProps(),