fix(programmer): reassignment while paused must not open new segment

Capture whether segment was running before reassignment, and only reopen
for new assignee if it was. A paused task that gets reassigned should not
start accruing time for the new assignee until explicitly resumed.

Also add test: reassignment while paused does not open segment.

Co-Authored-By: claude-flow <ruv@ruv.net>

test/programmer_daily_time_test.dart

@@ -235,4 +235,33 @@ void main() {
     final result = dailySecondsByAssignee(task: task, logs: logs, now: now);
     expect(result['a']![DateTime.utc(2026, 9, 27)], 3600); // not 6 hours
   });
+
+  test('reassignment while paused does not open a new segment for the new assignee', () {
+    // task: started 09:00, paused 10:00, reassigned {assignee_id:'b'} 11:00, completed 12:00 (all Sep 27)
+    // expected: a -> 3600s (09-10), b -> 0 (no interval opened after paused reassignment)
+    final task = _task(
+      status: ProgrammerTaskStatus.completed,
+      creatorId: 'a',
+      assigneeId: 'b',
+      startedAt: AppTime.fromComponents(year: 2026, month: 9, day: 27, hour: 9),
+      completedAt:
+          AppTime.fromComponents(year: 2026, month: 9, day: 27, hour: 12),
+    );
+    final logs = [
+      _ev('started', 27, 9),
+      _ev('paused', 27, 10),
+      _ev('reassigned', 27, 11, 0, {'assignee_id': 'b'}),
+      _ev('completed', 27, 12),
+    ];
+    final now =
+        AppTime.fromComponents(year: 2026, month: 9, day: 27, hour: 20);
+
+    final result = dailySecondsByAssignee(task: task, logs: logs, now: now);
+    expect(result['a']![DateTime.utc(2026, 9, 27)], 3600); // a worked 09-10
+    // b should have no time, or null entry
+    expect(
+      result['b']?[DateTime.utc(2026, 9, 27)] ?? 0,
+      0,
+    );
+  });
 }