pymongo + update n arrays from a document

I have a document in mongoDB like this :

{
  "_id" : 0,
  "name" : "Sponge Bob",
  "values" : [ [10000, 90], [10001, 92]  . . .],
  "storages" : [{ "number" : 123, "timestamp": "2022-09-08"}, . . .],
  "timestamp" : "2022-09-08"
} 

I want to delete a filtered "storages" objects filtered with a range date, the same thing to "values", but with the number on the first element of the array.

I've trying to do something like :

objects.update({"_id":1}, {"$pull" : {"timestamp" :{"$gt": date}}})

But I do realize that the "$pull" method in this case will not catch all the array of an object, but indeed all the document that will be filtered in that range filter.

So the question is : how do I do this kind of filter to this kind of elements inside the documents with pymongo ?