The $search extension will eventually need the shardId in order to pass it to external infrastructure (see context below). Currently, the only shard information that an extension has access to is the inRouter flag to distinguish between mongos and mongod, but this does not identify which shard a mongod belongs to.

Goal: Add a shardId field to the context that is passed to an extension during the AstNode to LogicalStage transformation (bind).

Context: https://docs.google.com/document/d/18VUMkOxYZl8g350eSEZ2Pwsv3MOjePmKanjdtwDiock/edit?disco=AAAB0uH_AUU