Fix flaky stats-batch tests and extend Crucible E2E LOTL coverage.

Stop the stats batch timer in unit tests before reading pending coalesced state, teach the Playwright stub agent to emit lotl_tier stats, and prefer server/webroot so phase-8 E2E serves the current frontend build.

server/internal/api/websocket_test.go

@@ -683,6 +683,8 @@ func TestMiningStatusRelayCoalescedToStatsBatch(t *testing.T) {
 	if err := connB.WriteJSON(Message{Type: "mining_fallback", Payload: payloadB}); err != nil {
 		t.Fatal(err)
 	}
+	stopStatsBatchTimer(hub)
+	hub.flushStatsBatch()
 
 	select {
 	case r := <-batchCh:
@@ -721,6 +723,17 @@ func TestMiningStatusRelayCoalescedToStatsBatch(t *testing.T) {
 	}
 }
 
+// stopStatsBatchTimer cancels the 250ms flush timer so tests can read statsBatch
+// without racing flushStatsBatch clearing the pending map.
+func stopStatsBatchTimer(hub *WSHub) {
+	hub.statsBatchMu.Lock()
+	defer hub.statsBatchMu.Unlock()
+	if hub.statsBatchTimer != nil {
+		hub.statsBatchTimer.Stop()
+		hub.statsBatchTimer = nil
+	}
+}
+
 func TestStatsBatchCoalescesSameAgent(t *testing.T) {
 	hub := NewWSHub(nil)
 	hub.queueStatsBroadcast(map[string]interface{}{
@@ -729,11 +742,13 @@ func TestStatsBatchCoalescesSameAgent(t *testing.T) {
 	hub.queueStatsBroadcast(map[string]interface{}{
 		"agent_id": "a1", "hashrate_15s": 99.0, "active_method": "inprocess",
 	})
+	stopStatsBatchTimer(hub)
 	hub.flushStatsBatch()
 
 	// Merged coalesce — later keys overwrite, earlier keys preserved.
 	hub.queueStatsBroadcast(map[string]interface{}{"agent_id": "a1", "hashrate_15s": 10.0, "lotl_tier": "cpu_inprocess"})
 	hub.queueStatsBroadcast(map[string]interface{}{"agent_id": "a1", "mining_hashrate": 850.0})
+	stopStatsBatchTimer(hub)
 	hub.statsBatchMu.Lock()
 	if len(hub.statsBatch) != 1 {
 		t.Fatalf("expected 1 agent in batch map, got %d", len(hub.statsBatch))
@@ -755,6 +770,7 @@ func TestStatsBatchCoalescesSameAgent(t *testing.T) {
 
 	hub.queueStatsBroadcast(map[string]interface{}{"agent_id": "a1", "hashrate_15s": 1.0})
 	hub.queueStatsBroadcast(map[string]interface{}{"agent_id": "a1", "hashrate_15s": 2.0})
+	stopStatsBatchTimer(hub)
 	hub.statsBatchMu.Lock()
 	if len(hub.statsBatch) != 1 {
 		t.Fatalf("expected 1 agent in batch map, got %d", len(hub.statsBatch))
@@ -780,6 +796,7 @@ func TestStatsBatchCoalescesLotlAttempts(t *testing.T) {
 		},
 	})
 	hub.queueStatsBroadcast(map[string]interface{}{"agent_id": "a2", "mining_hashrate": 1200.0})
+	stopStatsBatchTimer(hub)
 	hub.statsBatchMu.Lock()
 	var merged map[string]interface{}
 	if err := json.Unmarshal(hub.statsBatch["a2"], &merged); err != nil {