Database

[{server:{_id:"6108d87b9255993b26796ca9",version:"2.0.366",name:"aaaaaa",variables:[{key:"aKey",value:"aVal",},{key:"bKey",value:"bVal",},{key:"cKey",value:"cVal",}],__v:0}}]

Query

db.collection.aggregate({"$set":{"bucketName":{"$cond":{"if":{"$in":["aKey","$server.variables.key"]},"then":"aKey","else":"NOT_FOUND"}}}})

Result