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/context.rs

@@ -112,29 +112,14 @@ pub fn irc_digest() -> String {
 
 /// Build full context string for a prompt.
 /// notification_text is passed in from the notify module.
-pub fn build(include_irc: bool, notification_text: &str) -> String {
-    let mut parts = Vec::new();
-
-    let git = git_context();
-    if !git.is_empty() {
-        parts.push(format!("Context: {git}"));
+pub fn build(_include_irc: bool, notification_text: &str) -> String {
+    // Keep nudges short — Claude checks notifications via
+    // `poc-daemon status` on its own. Just mention the count.
+    let count = notification_text.matches("[irc.").count()
+        + notification_text.matches("[telegram.").count();
+    if count > 0 {
+        format!("{count} pending notifications")
+    } else {
+        String::new()
     }
-
-    let ws = work_state();
-    if !ws.is_empty() {
-        parts.push(ws);
-    }
-
-    if !notification_text.is_empty() {
-        parts.push(notification_text.to_string());
-    }
-
-    if include_irc {
-        let irc = irc_digest();
-        if !irc.is_empty() {
-            parts.push(irc);
-        }
-    }
-
-    parts.join("\n")
 }