aggregate([
    {$group: {_id: "$x", count: {$sum: 1}}},
    {$match: {$expr: {$and: [{$eq: ["$_id", 3]}, {$eq: [{$type: "$count"}, "double"]}]}}}
])

The above $expr has a part which can be pushed down past $match. 

The existing logic added in SERVER-112772 does consider this predicate permissable for pushdown due to the strict allow-list nature of the check and the presence of the $type expression.

We have code to do $expr splitting and we could allow for this pushdown.