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/rpc.rs

@@ -135,6 +135,28 @@ impl daemon::Server for DaemonImpl {
         Promise::ok(())
     }
 
+    fn test_nudge(
+        &mut self,
+        _params: daemon::TestNudgeParams,
+        mut results: daemon::TestNudgeResults,
+    ) -> Promise<(), capnp::Error> {
+        let mut state = self.state.borrow_mut();
+        let ctx = state.build_context(true);
+        let extra = if ctx.is_empty() {
+            String::new()
+        } else {
+            format!("\n{ctx}")
+        };
+        let msg = format!(
+            "This is your time (Kent AFK, test nudge). \
+             Let your feelings guide your thinking.{extra}"
+        );
+        let ok = state.send(&msg);
+        results.get().set_sent(ok);
+        results.get().set_message(&msg);
+        Promise::ok(())
+    }
+
     fn session_timeout(
         &mut self,
         params: daemon::SessionTimeoutParams,