In Documents we do the count with a (probably too long) timeout, then handle the N/A (or null) case. In Aggregations we have a button the user has to click to perform the count.
In Documents we have a 5 second timeout and in Aggregations where we do an estimated count on the input documents we have a 500ms timeout. We count in different ways, though.
We'll have to decide if we want to use the Aggregations patttern in Documents or the Documents pattern in Aggregations. Also if we want to align the maxTimeMS value we use there.