Category Schema

import mongoose, { InferSchemaType, Model, model, Schema, Types, models } from "mongoose";
import type { Course } from "./course.model";
export type Category = InferSchemaType<typeof categorySchema> & {_id: Types.ObjectId;};
export const category = {model: "Category",collection: "categorys",} as const;
const categorySchema = new Schema({
name: { type: String, unique: true },
courses: [{ type: Schema.Types.ObjectId, ref: 'Course' }],
},{ 
collection: category.collection, timestamps: true 
});
categorySchema.index({ name: 1 });

const CategoryModel: Model<Category> =models?.[category.model] || model<Category>(category.model, categorySchema);

export default CategoryModel;

PATCH route :

import { currentUser } from "@/lib/auth";
import CategoryModel from "@/models/category.model";
import CourseModel from "@/models/course.model";
import { NextResponse } from "next/server"; import {Mongoose} from "mongoose";

export async function PATCH( req: Request, { params }: { params: { courseId: string } } ) { try { const session = await currentUser(); const { courseId } = params; 

const values = await req.json();
console.log(values.categoryId);

if (!session) {
  return new NextResponse("Unauthorized", { status: 401 });
}
const course = await CourseModel.findById({
  _id: courseId || params.courseId,
});

console.log(course?.id);

const selectedCategoryId = values.categoryId;
const initialCategoryId = course?.categoryId;

if (selectedCategoryId !== initialCategoryId) {
  await Promise.all([
    await CourseModel.findByIdAndUpdate(
      {
        _id: courseId || params.courseId,
        userId: session.id,
      },
      { $set: { ...values } },
      { new: true }
    ),
    await CategoryModel.findByIdAndUpdate(
      {
        _id: initialCategoryId,
      },
      { $pull: { courses: course?._id } },
      { new: true }
    ),
    await CategoryModel.findByIdAndUpdate(
      {
        _id: selectedCategoryId,
      },
      { $push: { courses: courseId } },
      { new: true }
    ),
  ]);
  return NextResponse.json("Updated");
}

return NextResponse.json("Not Updated");
} 
catch (error) 
{console.error("[Courses]", error);return new NextResponse("Internal Error", { status: 500 });}}

i want to add courseId or course?._id into courses array in category Schema

I tried mongoose.Types.ObjectId, but all the methods i have used are creating new objectId instead of adding the course id into courses array, i am seding course id as params to the patch request, please help me with this, do i need change the schema or is it fine?, if i change the array into array of strings, the issue might get solved but i want to have a relation between course and category schema