Refactor $search/$vectorSearch LiteParsed handling so that the public LiteParsedSearch stage desugars into two internal LiteParsed stages: LiteParsedInternalSearchMongotRemote and LiteParsedInternalSearchIdLookup. After desugaring, only the internal stages should remain in the pipeline. This will allow us to use custom view policy callbacks for $search/vectorSearch.

This ticket also involves ensuring search-on-views works end to end, as well as removing special case search logic from runAggregate() when possible.