fix: reset startTime on task assignment for accurate duration tracking

Problem:
Stale worker detection was reporting incorrect durations when sessions
were reused. Workers showed total session lifetime rather than time
since current task assignment.

Example:
- Session created 13 hours ago for issue #71
- Session reused 4 minutes ago for issue #106
- Status incorrectly showed: "DEV active on #106 (3.3h)"
- Should show: "DEV active on #106 (4m)"

Root Cause:
In recordWorkerState(), startTime was only set when spawning a new
session (sessionAction === 'spawn'). When reusing an existing session
(sessionAction === 'send'), the old startTime persisted, causing
stale worker detection to use total session age instead of task age.

Solution:
Always set startTime to current time when activating a worker,
regardless of whether we're spawning a new session or reusing one.
The startTime field now consistently represents "when did this worker
start THIS specific task" rather than "when was the session created".

Changes:
- lib/dispatch.ts: Move startTime assignment outside spawn-only block
- startTime now set unconditionally for both spawn and send actions
- Maintains backward compatibility with existing health checks

Impact:
- Stale worker detection now accurately reflects task duration
- Session reuse no longer causes false positive stale alerts
- Duration shown in status matches actual time on current task

Addresses issue #108

lib/dispatch.ts

@@ -244,12 +244,13 @@ async function recordWorkerState(
   workspaceDir: string, groupId: string, role: "dev" | "qa",
   opts: { issueId: number; tier: string; sessionKey: string; sessionAction: "spawn" | "send" },
 ): Promise<void> {
-  const params: { issueId: string; tier: string; sessionKey?: string; startTime?: string } = {
+  const params: { issueId: string; tier: string; sessionKey?: string; startTime: string } = {
-    issueId: String(opts.issueId), tier: opts.tier,
+    issueId: String(opts.issueId),
+    tier: opts.tier,
+    startTime: new Date().toISOString(), // Always reset startTime for new task assignment
   };
   if (opts.sessionAction === "spawn") {
     params.sessionKey = opts.sessionKey;
-    params.startTime = new Date().toISOString();
   }
   await activateWorker(workspaceDir, groupId, role, params);
 }