Treat background finalization as another GC task so it won't run in parallel with the marker.

runtime/vm/service.cc

Index: runtime/vm/service.cc
diff --git a/runtime/vm/service.cc b/runtime/vm/service.cc
index fe730422d6ba4f73e48fe958c18db9e6b6227ba4..104d22c4bb448658f790e8c91288bf5047522100 100644
--- a/runtime/vm/service.cc
+++ b/runtime/vm/service.cc
@@ -3548,6 +3548,10 @@ class PersistentHandleVisitor : public HandleVisitor {
   }
 
   void Append(FinalizablePersistentHandle* weak_persistent_handle) {
+    if (!weak_persistent_handle->raw()->IsHeapObject()) {
+      return;  // Free handle.
+    }
+
     JSONObject obj(handles_);
     obj.AddProperty("type", "_WeakPersistentHandle");
     const Object& object =