Hello @Stefan_Tesoi, welcome to the MongoDB Community Forum!
Your query looks just about correct as per this documentation example: Query an Array of Embedded Documents - A Single Nested Document Meets Multiple Query Conditions on Nested Fields.
You can use projection : Project Specific Array Elements in the Returned Array. The documentation also says:
See the aggregation operator
$filterto return an array with only those elements that match the specified condition.
Here are posts with similar question and use $filter: