Problem with mongoose and push methods with typescript

I have a problem with push method with typescript with error ("Property 'push' does not exist on type 'ObjectId'.ts(2339)") and also have this error with user // Object is possibly 'null'.ts(2531) // and try this code in javascript and it's work fine but in Typescript not with 3 errors of user and push method.. and how we can add populate to add new post with user id attached to post schema.. and thank you in advance.

controller/feed.ts

     export const createPost: RequestHandler = (req, res, next) => {
  const errors = validationResult(req);
  if (!errors.isEmpty()) {
    const error = new Error("Validation failed, entered data is incorrect.");
    error.statusCode = 422;
    throw error;
  }
  if (!req.file) {
    const error = new Error("No image provided.");
    error.statusCode = 422;
    throw error;
  }
  const imageUrl = req.file.path;
  const title = req.body.title;
  const content = req.body.content;
  let creator;
  const post = new Post({
    _id: new mongoose.Types.ObjectId(),
    title: title,
    content: content,
    imageUrl: imageUrl,
    creator: req.userId,
  });
  console.log(req.params.userId);
  post
    .save()
    .then((result) => {
      return User.findById(req.userId);
    })

    .then((user) => {
      creator = user;
      *user?*.posts.push(post);    // error: Property 'push' does not exist on type 'ObjectId'.ts(2339)

// user without ? i have this error : Object is possibly 'null'.ts(2531)
      return user?.save();
    })
    .then((result) => {
      res.status(201).json({
        message: "Post created successfully!",
        post: post,
        creator: { _id: creator._id, name: creator.name },
      });
    })
    .catch((err) => {
      if (!err.statusCode) {
        err.statusCode = 500;
      }
      next(err);
    });
};

user.model.ts

import { model,Schema, Document,Types } from "mongoose";

export interface IUser extends Document {
  email: string;
  password: string;
  name: string;
  status: string;
  posts: Types.ObjectId;
  createdAt?: Date;
  updatedAt?: Date;
}

const userSchema: Schema = new Schema(
  {
    _id: Schema.Types.ObjectId,
    email: {
      type: Schema.Types.String,
      required: true,
    },
    password: {
      type: Schema.Types.String,
      required: true,
    },
    name: {
      type: Schema.Types.String,
      required: true,
    },
    status: {
      type: Schema.Types.String,
      default: "I am new!",
    },
    posts: {
      type: Schema.Types.ObjectId,
      ref: "Post",
    },
  },
  { timestamps: true, versionKey: false }
);

const User = model<IUser>("User", userSchema);
export default User;

export {};

post.model.ts

import { model,Schema, Document,Types } from "mongoose";

export interface IPost extends Document {
  title: string;
  imageUrl: string;
  content: string;
  creator: Types.ObjectId;
}
const postSchema = new Schema(
  {
    _id: Schema.Types.ObjectId,
    title: {
      type: Schema.Types.String,
      required: true,
    },
    imageUrl: {
      type: Schema.Types.String,
      required: true,
    },
    content: {
      type: Schema.Types.String,
      required: true,
    },
    creator: {
      type: Schema.Types.ObjectId,
      ref: "User",
      required: true,
    },
  },
  { timestamps: true, versionKey: false }
);

const Post = model<IPost>("Post", postSchema);
export default Post;

export {};