made some progress in saving and restoring the state during the simulation, with identical results.

Option to de/serialize btPersistentContactManifolds and fix lossy conversion during btMultiBody de/serialization of base world transform
(serialize the quaternion, not the converted 3x3 matrix)
There are still several caches not taken into account, and btMultiBody links/constraints are not deserialized yet etc.
See examples\pybullet\examples\saveRestoreState.py for an example.

src/BulletDynamics/Featherstone/btMultiBodyDynamicsWorld.cpp

@@ -972,6 +972,8 @@ void	btMultiBodyDynamicsWorld::serialize(btSerializer* serializer)
 
 	serializeCollisionObjects(serializer);
 
+	serializeContactManifolds(serializer);
+
 	serializer->finishSerialization();
 }