Relation between $$CLUSTER_TIME and corresponding changeEvent.clusterTime

Let’s imagine that I am updating a document with a pipeline instead of modifier and I am using $$CLUSTER_TIME variable to record the time when the update happened. For example:

db.myCollection.update({}, [{ $set: { updatedTs: '$$CLUSTER_TIME } }]);

If I am also observing the same collection with a changes stream, the above operation will result in a change event which will have its own clusterTime property. I already know that it will not be the same as the value of updatedTs, but I am wondering if mongo can guarantee any relation between the two values. For example, is it correct to assume that the high component of the corresponding Timestamp objects will be the same for both updatedTs and changeEvent.clusterTime?

Unfortunately, the experimentation shows that there can be no connection at all. I guess the only thing one can assume is that $$CLUSTER_TIME will always be smaller than changeEvent.clusterTime, but I am not even sure if $$CLUSTER_TIME will be monotonic as a function of changeEvent.clusterTime, i.e. given two subsequent operations with clusterTime1 < clusterTime2, can one expect that the corresponding updatedTs (as in the example above) will also satisfy < or (at least <=) condition?