Thanks to David Osborne's comments above, I was able to do a little more research and come up with an answer. It turns out simple LINQ queries do in fact translate directly to native Mongo queries and not to $where queries.
var filter = Builders<BsonDocument>.Filter.Where(x => x["status"] != "ready");
var findFluent = collection.Find(filter);
Console.WriteLine(findFluent);
filter = Builders<BsonDocument>.Filter.Ne("status", "ready");
var findFluent = collection.Find(filter);
Console.WriteLine(findFluent);
Both print out the identical queries. This holds for simple combinations of equality and logical operators.
However, some operators appear to be inaccessible through LINQ. I attempted to write an $in query
var success = new List<string> { "imported", "processed" };
var filter = Builders<BsonDocument>.Filter.Where(x => success.Contains(x["status"].ToString()));
and got a runtime error. Similarly with a regex match
var regex = new Regex("^*0000");
var filter = Builders<BsonDocument>.Filter.Where(x => regex.IsMatch(x["orderId"].ToString()));
Not surprising but good to know.