poc-daemon: fix idle nudge and notification delivery

- Strip context bloat from nudge messages — no more IRC digest, git
  log, or work state inlined into tmux send-keys (was silently dropping
  the entire message). Nudge now just includes pending notification count.
- Notifications no longer send directly via tmux — they flow through
  the idle nudge only. Urgent notifications reset the fired flag so
  the nudge fires sooner.
- Add test-nudge RPC that exercises the actual daemon send path
  (test-send was client-side only, didn't test the real code path).
- Update nudge text: "Let your feelings guide your thinking."
- Increase send-keys sleep from 200ms to 500ms.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

poc-daemon/src/tmux.rs

@@ -44,7 +44,7 @@ pub fn send_prompt(pane: &str, msg: &str) -> bool {
     if !ok {
         return false;
     }
-    thread::sleep(Duration::from_millis(200));
+    thread::sleep(Duration::from_millis(500));
 
     // Submit
     Command::new("tmux")