Database

[{id:0,germanTranslations:["Diagnosekit","Testkit"]},{id:1,germanTranslations:["Ausprobieren","Testen","Probe","Test","Versuch"]},{id:2,germanTranslations:["Testament","Bibel"]}]

Query

db.collection.aggregate([{$match:{germanTranslations:{$regex:"^test",$options:"i"}}},{$unwind:"$germanTranslations"},{$match:{germanTranslations:{$regex:"^test",$options:"i"}}},{$project:{"germanTranslations":1,"result_length":{$strLenCP:"$germanTranslations"}}},{$sort:{"result_length":1}}])

Result