No need to set permissions when Docerizing Laravel App?

I've been following Andrew Schmelyun's course with Docker and everything looks normal to what I do in non-dockerized environment. However, I used to set the permissions of the project directory like this:

# Assuming project src is in /var/www
chown -R www-data:www-data /var/www
chmod -R 755 /var/www
find /var/www/ -type f -exec chmod 644 {} \;
chmod 600 /var/www/.env
chmod -R 755 /var/www/storage
chmod -R 755 /var/www/bootstrap/cache

In Andrew's course, there are no mention of permissions. Does Docker handle that out of the box? This is my final compose file from the course:

services:
  php:
    build:
      context: .
      dockerfile: php/php.dockerfile
      args:
        - HOST_UID=1000
        - HOST_GID=1000
    volumes:
      - ./src:/var/www/html

  nginx:
    build:
      context: .
      dockerfile: nginx/nginx.dockerfile
      args:
        - HOST_UID=1000
        - HOST_GID=1000
    ports:
      - 80:80
    volumes:
      - ./src:/var/www/html
    depends_on:
      - mysql
      - php

  mysql:
    image: mysql:latest
    ports:
      - 3306:3306
    environment:
      - MYSQL_DATABASE=laravel
      - MYSQL_USER=laravel
      - MYSQL_PASSWORD=secret
      - MYSQL_ROOT_PASSWORD=secret
    volumes:
      - ./mysql:/var/lib/mysql

  composer:
    build:
      context: .
      dockerfile: composer/composer.dockerfile
      args:
        - HOST_UID=1000
        - HOST_GID=1000
    volumes:
      - ./src:/var/www/html
    working_dir: /var/www/html

  npm:
    image: node:current-alpine
    volumes:
      - ./src:/var/www/html
    working_dir: /var/www/html
    entrypoint: ["npm"]

  artisan:
    build:
      context: .
      dockerfile: php/php.dockerfile
      args:
        - HOST_UID=1000
        - HOST_GID=1000
    volumes:
      - ./src:/var/www/html
    working_dir: /var/www/html
    depends_on:
      - mysql
    entrypoint: ["php", "/var/www/html/artisan"]