Query using $gte and New Date() working in MongoDB shell but not through python pymongo
As per MongoDB pymongo documentation here

The  count() method is deprecated and not supported in a transaction. Please use count_documents() instead.

count(with_limit_and_skip=False)

DEPRECATED - Get the size of the results set for this query.

The count() method is deprecated and not supported in a transaction. Returns the number of documents in the results set for this query. Does not take limit() and skip() into account by default - set with_limit_and_skip to True if that is the desired behavior. Raises OperationFailure on a database error.

When used with MongoDB &gt;= 2.6, count() uses any hint() applied to the query. In the following example the hint is passed to the count command:

collection.find({‘field’: ‘value’}).hint(‘field_1’).count()


The count() method obeys the read_preference of the Collection instance on which find() was called.

Changed in version 3.7: Deprecated.
Changed in version 2.8: The count() method now supports hint().

count_documents(filter, session=None, kwargs)

Count the number of documents in this collection.

The count_documents() method is supported in a transaction.

All optional parameters should be passed as keyword arguments to this method. Valid options include:


skip (int): The number of matching documents to skip before returning
results.
limit (int): The maximum number of documents to count.
maxTimeMS (int): The maximum amount of time to allow this operation
to run, in milliseconds.
collation (optional): An instance of <a
href="https://api.mongodb.com/python/current/api/pymongo/collation.html#pymongo.collation.Collation" rel="nofollow noreferrer">
Collation. This option is only supported on MongoDB 3.4 and
above.
hint (string or list of tuples): The index to use. Specify either the
index name as a string or the index specification as a list of tuples
(e.g. [(‘a’, pymongo.ASCENDING), (‘b’, pymongo.ASCENDING)]). This
option is only supported on MongoDB 3.6 and above.


The count_documents() method obeys the read_preference of this Collection.

Note When migrating from count() to count_documents() the following query operators must be replaced:

Operator     Replacement
$where        $expr
$near         $geoWithin with $center
$nearSphere $geoWithin with $centerSphere

$expr requires MongoDB 3.6+


For your further ref here and here