Tasks visibly progress: Run → In Progress (+ close drawer); approve → In Review

A task assigned to an agent never moved, so it looked like nothing happened. Now:
- Clicking Run moves the task from Backlog to In Progress and closes the drawer.
- When an approved artifact lands on a task, it moves to In Review (unless already Done),
  so the delivered result is visible on the board instead of sitting in Backlog.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

client/src/pages/BoardPage.tsx

@@ -512,14 +512,18 @@ function TaskDrawer({
               <Button
                 disabled={busy || !seatId}
                 onClick={() =>
-                  act(
-                    () => api.post('/api/assembler/runs', { seatId, workItemId: task.id }),
-                    'Dispatched — it will appear in the review inbox shortly.',
-                  ).then(() => {
-                    // The proposal lands ~a few seconds later; nudge the review badge to refetch.
+                  act(async () => {
+                    await api.post('/api/assembler/runs', { seatId, workItemId: task.id })
+                    // Visible feedback: the task leaves Backlog for In Progress while the agent works.
+                    if (task.status === 'Backlog') {
+                      await api.patch(`/api/orgboard/tasks/${task.id}/move`, { status: 'InProgress' })
+                    }
+                  }, 'Sent to the agent — moved to In Progress; its result will land in the review inbox.').then(() => {
+                    // The proposal lands a few seconds later; nudge the review badge, then close.
                     window.dispatchEvent(new Event(REVIEWS_CHANGED))
                     setTimeout(() => window.dispatchEvent(new Event(REVIEWS_CHANGED)), 4000)
                     setTimeout(() => window.dispatchEvent(new Event(REVIEWS_CHANGED)), 9000)
+                    onClose()
                   })
                 }
               >