Database

db={bookings:[{vehicle_id:ObjectId("6307d365fe35112dcd313bdf"),start_date:ISODate("2022-10-11T02:28:30.037Z"),end_date:ISODate("2022-10-12T02:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bdf"),start_date:ISODate("2022-10-12T02:28:30.037Z"),end_date:ISODate("2022-10-13T02:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bdd"),start_date:ISODate("2022-10-17T02:28:30.037Z"),end_date:ISODate("2022-10-22T02:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bdd"),start_date:ISODate("2022-10-10T04:28:30.037Z"),end_date:ISODate("2022-10-11T03:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bdc"),start_date:ISODate("2022-10-09T02:28:30.037Z"),end_date:ISODate("2022-10-13T00:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bdb"),start_date:ISODate("2022-10-11T06:28:30.037Z"),end_date:ISODate("2022-10-11T00:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bda"),start_date:ISODate("2022-10-12T02:28:30.037Z"),end_date:ISODate("2022-10-13T02:28:30.037Z")},{vehicle_id:ObjectId("6307d365fe35112dcd313bde"),start_date:ISODate("2022-10-07T02:28:30.037Z"),end_date:ISODate("2022-10-11T02:28:30.037Z")}],vehicles:[{_id:ObjectId("6307d365fe35112dcd313bdf"),model:"Hyundai Tucson"},{_id:ObjectId("6307d365fe35112dcd313bdd"),model:"Ferrari"},{_id:ObjectId("6307d365fe35112dcd313bdc"),model:"Lamborghini"},{_id:ObjectId("6307d365fe35112dcd313bdb"),model:"McLaren"},{_id:ObjectId("6307d365fe35112dcd313bda"),model:"Bugatti"},{_id:ObjectId("6307d365fe35112dcd313bde"),model:"Aston Martin"}]}

Query

db.vehicles.aggregate([{$lookup:{from:"bookings",let:{vehicle_id:"$_id"},pipeline:[{$match:{$expr:{$and:[{$or:[{$and:[{$lt:["$start_date",ISODate("2022-10-12T02:28:30.037Z")]},{$gte:["$start_date",ISODate("2022-10-11T02:28:30.037Z")]}]},{$and:[{$lte:["$start_date",ISODate("2022-10-11T02:28:30.037Z")]},{$gt:["$end_date",ISODate("2022-10-11T02:28:30.037Z")]}]}]},{$eq:["$vehicle_id","$$vehicle_id"]}]}}}],as:"res"}},{$match:{"res.0":{$exists:false}}},{$unset:"res"}])

Result