Mongo Playground

Configuration

[{"_id":{"$oid":"63267309592e38db589c576d"},"name":"ASOS DESIGN tapered smart shorts in white and navy stripe","color predictions":[{"Beige":{"$numberInt":"1"}},{"Black":{"$numberInt":"2"}},{"White":"1"}],"color":"Black"},{"_id":{"$oid":"84253452492e38db589c576d"},"name":"ASOS DESIGN tapered smart shorts in white and navy stripe","color predictions":[{"Brown":{"$numberInt":"3"}},{"Green":{"$numberInt":"1"}},{"Navy Blue":"1"}],"color":"Brown"}]

Query

db.collection.aggregate([{$set:{colorPredictions:{$reduce:{input:{"$getField":"color predictions"},initialValue:[],in:{"$concatArrays":["$$value",{$objectToArray:"$$this"}]}}}}},{$match:{"colorPredictions.k":{$in:["Brown","Navy Blue"]/** Search filter*/}}},{$unset:"colorPredictions"}])

Result