import { isEqual } from "lodash-es";
import { ObjectId } from "mongodb";
import { EJSON, ObjectId as BSONObjectId } from "bson"

const id1 = new ObjectId("667ffeda8515296ac46b1644");
const id2 = new ObjectId("667ffeda8515296ac46b1644");
const id3 = new BSONObjectId("667ffeda8515296ac46b1644");

// output true
console.log(isEqual(id1, id2))

// output true
console.log(
    isEqual(
        EJSON.parse(EJSON.stringify(id1)),
        EJSON.parse(EJSON.stringify(id2))
    )
);

// output false
console.log(
    isEqual(
        id1,
        EJSON.parse(EJSON.stringify(id2))
    )
);

// output true
console.log(
    isEqual(
        id3,
        EJSON.parse(EJSON.stringify(id2))
    )
);

The issue is a bit perplexing, but it looks like it's about a nuance of the lodash-es package. Please take a look at the following comparisons:

const id2 = new ObjectId("667ffeda8515296ac46b1644");
const id2_parsed = EJSON.parse(EJSON.stringify(id2));
const id3 = new BSONObjectId("667ffeda8515296ac46b1644");

console.log(id2.equals(id3));
console.log(id2_parsed.equals(id3));
console.log(id2.equals(id2_parsed));

console.log();

console.log(isEqual(id2, id3));
console.log(isEqual(id2_parsed, id3));
console.log(isEqual(id2, id2_parsed));

true
true
true

false
true
false

import { isEqual } from "lodash-es";
import { ObjectId } from "mongodb";
import { EJSON, ObjectId as BSONObjectId, BSON } from "bson"

const objId = new ObjectId("667ffeda8515296ac46b1644");
const bsonId = new BSONObjectId("667ffeda8515296ac46b1644");

// false
console.log(
    isEqual(
        objId,
        bsonId
    )
)

// true
console.log(
    isEqual(
        EJSON.parse(EJSON.stringify(objId)),
        EJSON.parse(EJSON.stringify(bsonId)),
    )
)

// false (because EJSON.parse uses internal bson ObjectId instance with fromExtendedJSON)
console.log(
    isEqual(
        objId,
        EJSON.parse(EJSON.stringify(bsonId)),
    )
)

// true (because EJSON.parse uses internal ObjectId instance with fromExtendedJSON)
console.log(
    isEqual(
        EJSON.parse(EJSON.stringify(objId)),
        bsonId
    )
)

// true (because we override bson ObjectId instance with fromExtendedJSON from mongodb ObjectId instance)

BSONObjectId.fromExtendedJSON = ObjectId.fromExtendedJSON;

console.log(
    isEqual(
        objId,
        EJSON.parse(EJSON.stringify(bsonId)),
    )
)

// false because of the previous reason
console.log(
    isEqual(
        EJSON.parse(EJSON.stringify(objId)),
        bsonId
    )
)