docs: M5d-1 checklist fixes before hand-over

Given tests: Action::Turn (not To), send_turn of epoch 1, clippy on
compact_summary, jsonl-without-baseline, live turn after compact sends
the carry. send_turn maps Damaged to Local("log") as read_turn did.
Gate counts 1484 → 1508. Mutations recorded in the README.

Co-Authored-By: Grok 4.6 <noreply@x.ai>

docs/plans/M5d1/files/crates/loopd/tests/compact_turn.rs

@@ -3,7 +3,7 @@
 mod support;
 
 use bxcore::{Epoch, LogRecord, SessionId, TurnEvent};
-use loopd::baseline::Baseline;
+use loopd::baseline::{Baseline, CARRY_HEADING};
 use loopd::compact;
 use loopd::llama::Client;
 use loopd::memory::NoMemory;
@@ -125,11 +125,31 @@ fn usage_at_the_threshold_compacts_before_the_turn_returns() {
     w.finish(&mut s, "hi", outcome).unwrap();
     assert_eq!(s.epoch(), Epoch(1));
     assert_eq!(s.carry(), Some("the sum"));
+    w.server.route(CHAT, vec![sse("next", 0, 20)]);
+    let mut events = Vec::new();
+    run_turn(&mut s, &w.runtime(), "again", None, &mut |e| {
+        events.push(e.clone())
+    })
+    .unwrap();
     let sent = w.server.requests_to(CHAT);
-    assert_eq!(sent.len(), 2);
+    assert_eq!(sent.len(), 3);
     assert_eq!(sent[0].json()["id_slot"], 0);
     assert_eq!(sent[1].json()["id_slot"], 1);
     assert!(sent[1].json().get("tools").is_none());
+    let live = sent[2].json();
+    assert_eq!(live["id_slot"], 0);
+    let contents: Vec<&str> = live["messages"]
+        .as_array()
+        .unwrap()
+        .iter()
+        .map(|m| m["content"].as_str().unwrap_or(""))
+        .collect();
+    assert!(
+        contents
+            .iter()
+            .any(|c| c.contains(CARRY_HEADING) && c.contains("the sum")),
+        "{contents:?}"
+    );
     let old = w.home.records("a");
     assert!(matches!(
         old.last(),