Database

[{"_id":1,"name":"C:"},{"_id":2,"parentFolderId":1,"name":"Users"},{"_id":3,"parentFolderId":2,"name":"<username>"},{"_id":4,"parentFolderId":3,"name":"Desktop"},{"_id":5,"parentFolderId":4,"name":"alpha.tsx"},{"_id":6,"parentFolderId":1,"name":"Program Files"},{"_id":7,"parentFolderId":1,"name":"System32"},{"_id":8,"parentFolderId":1,"name":"Program Files(x86)"},{"_id":9,"parentFolderId":19,"name":"D"},{"_id":10,"parentFolderId":9,"name":"Program Files(x86)"},{"_id":11,"parentFolderId":10,"name":"prog"}]

Query

db.collection.aggregate([{$graphLookup:{from:"collection",startWith:"$parentFolderId",connectFromField:"parentFolderId",connectToField:"_id",as:"parents"}},{$match:{$expr:{$eq:[{$in:["C:","$parents.name"]},true]}}},{$unset:"parents"},{$set:{tags:["#new","#cool","#vibes"]}},{$merge:{into:"collection"}}])

Result