CB-598: track reminder counts per pending item, not per lead per source

Work that arrived during the ~15s push_backoff_ms window between two
ticks landed in the pending map before the next tick's start-of-tick
snapshot, so a shared per-lead-per-source counter (carried forward via
scheduleNext(lead, count+1, ...)) already treated it as exhausted
backlog even though no nudge had ever named it. ReplyPushLoop.tick now
recomputes each source's reminder count fresh every tick as the
minimum nudge count among that source's currently pending items, so a
freshly-arrived item (count 0) keeps its source eligible regardless of
how depleted an older, still-undrained sibling's count is. decide()
itself is unchanged.

bridged/src/test/java/dev/ltms/bridged/msg/ReplyPushLoopTest.java

@@ -42,6 +42,7 @@ class ReplyPushLoopTest {
 
     private static final String PRIMARY = "term_primary";
     private static final String WORKER = "term_worker";
+    private static final String WORKER2 = "term_worker2";
     private static final ObjectMapper MAPPER = new ObjectMapper();
 
     private PrimaryRegistry registry;
@@ -579,6 +580,83 @@ class ReplyPushLoopTest {
                 "both the reply and the ticket source are at their own cap — must still stop");
     }
 
+    // --- CB-598: work arriving during a backoff must not read as stale backlog -------------------
+
+    @Test
+    void aTargetArrivingDuringTheBackoffGetsNudgedDespiteAnAlreadyCappedSibling() {
+        // The bug: reminder counts used to be a single counter per lead per source, carried
+        // forward across scheduled ticks (scheduleNext(lead, count + 1, ...)) rather than tracked
+        // per pending item. WORKER gets nudged once here, which — with cap=1 — exhausts the
+        // shared reply-source counter for this lead. WORKER2 then queues a reply for the SAME
+        // lead "during the backoff": while the schedule from WORKER's tick is still active, before
+        // the next tick's own start-of-tick snapshot runs. At that next tick, the OLD code passed
+        // the already-exhausted shared counter into decide() regardless of WORKER2 never having
+        // been named in any nudge, and — because WORKER2 was already present in that tick's
+        // "before" snapshot — stopOrRestart's race check (proven correct on its own elsewhere in
+        // this file) does not save it either: it looks like ordinary stale backlog, not a race.
+        // WORKER2 was then stranded forever with no live schedule and no nudge ever naming it.
+        //
+        // tick() is driven directly (package-private, same reasoning as stopOrRestart being
+        // directly testable) so the exact interleaving is deterministic instead of racing the
+        // scheduler thread over a real ~15s backoff.
+        //
+        // Before the fix, this test fails on the second assertEquals: rec.sendCount() stays at 1
+        // (decide() returns STOP on the second tick(), so injectNudge is never called a second
+        // time) and the "must still get one" assertion never even runs.
+        int cap = 1;
+        var rec = recordingClient();
+        agents = new AgentControl(rec);
+        inbox.own(WORKER2);
+        inbox.publish(WORKER, "m1", "hello");
+        var loop = loop(cap, 100_000); // huge backoff — nothing fires on its own; we drive tick()
+
+        loop.onReplyQueued(WORKER);
+        loop.tick(PRIMARY); // first tick: nudges WORKER alone; WORKER's own count reaches the cap
+        assertEquals(1, rec.sendCount(), "the first tick should nudge about WORKER");
+
+        // WORKER2 "arrives during the backoff": queued for the same lead while the schedule from
+        // the tick above is still active (activeLeads still holds PRIMARY), before the next tick
+        // (simulated below) takes its own start-of-tick snapshot.
+        inbox.publish(WORKER2, "m2", "hello2");
+        loop.onReplyQueued(WORKER2);
+
+        loop.tick(PRIMARY); // the tick that would fire once that backoff elapsed
+
+        assertEquals(2, rec.sendCount(),
+                "WORKER2 was never named in any nudge yet and must still get one, even though "
+                        + "WORKER's own reminder count is already at the cap");
+        String secondNudge = rec.sentParams().get(1).getValue().toString();
+        assertTrue(secondNudge.contains(WORKER2), "the never-named target must be named: " + secondNudge);
+
+        // Criterion #3: isActive() must reflect that this lead still had a live nudge to give —
+        // the second tick took the INJECT branch, so the schedule stayed live rather than being
+        // torn down under WORKER2.
+        assertTrue(loop.isActive(), "the schedule must stay active after nudging the fresh target");
+    }
+
+    @Test
+    void aTicketArrivingDuringTheBackoffGetsNudgedDespiteAnAlreadyCappedSibling() {
+        // Mirrors the reply-side test above for the ticket source.
+        int cap = 1;
+        var rec = recordingClient();
+        agents = new AgentControl(rec);
+        var loop = loop(cap, 100_000);
+
+        loop.onTicketTerminal("task-1", WORKER, false);
+        loop.tick(PRIMARY); // first tick: nudges task-1 alone; its count reaches the cap
+        assertEquals(1, rec.sendCount(), "the first tick should nudge about task-1");
+
+        loop.onTicketTerminal("task-2", WORKER, false); // arrives during the backoff, same lead
+        loop.tick(PRIMARY);
+
+        assertEquals(2, rec.sendCount(),
+                "task-2 was never named in any nudge yet and must still get one, even though "
+                        + "task-1's reminder count is already at the cap");
+        String secondNudge = rec.sentParams().get(1).getValue().toString();
+        assertTrue(secondNudge.contains("task-2"), "the never-named ticket must be named: " + secondNudge);
+        assertTrue(loop.isActive(), "the schedule must stay active after nudging the fresh ticket");
+    }
+
     // --- metrics (CB-512) ----------------------------------------------------------------------
 
     @Test