Currently SBE handles only $lookup stages where the join is performed as an equi-join between localField and foreignField path expressions. The optimizer can extend this syntax to include also a pipeline holding a $match to be performed on the foreign collection to trim its results during the scan.

Improvement #1: convert the MatchExpression held by the $match stage into SBE code to be executed on top of the filtering done to enforce the equijoin constraint

Improvement #2: if the $match expression is an $expr with a single $eq, or a top-level $and with at least one $eq children, pull up those equalities and add them to the equijoin constraints (including declaring any required variable defined in the let field of the $lookup)