Pretty much yes, codeberg integrates some additional services and branding on top (such as codeberg-pages for static page hosting or forgejo-runners for CI) but you can integrate those yourself as well, it's just extra work.

If you're looking for an open alternative to github/gitlab codeberg is imo definitely the way to go

Incoming wall of text

Here is my install script to set up Ubuntu since it has a bit of extra steps for privileged ports https://gitlab.meme.beer/-/snippets/1

Docker compose example, note that my config has a shared network with containers in another compose called nginx to keep traffic inside docker.

name: "gitlab"
services:
  gitlab:
    image: 'gitlab/gitlab-ce:latest'
    #command: update-permissions
    restart: always
    hostname: 'gitlab.example.com'
    environment:
      GITLAB_OMNIBUS_CONFIG: |
        external_url 'https://gitlab.example.com'

        pages_external_url 'https://pages.example.com'
        pages_nginx['enable'] = true
        pages_nginx['listen_port'] = 6000
        pages_nginx['listen_https'] = false
        pages_nginx['redirect_http_to_https'] = false

        #puma['per_worker_max_memory_mb'] = 2048 # 2GB

        gitlab_rails['gitlab_email_from'] = 'gitlab@mailer.example.com'
        gitlab_rails['gitlab_email_display_name'] = 'GitLab'
        gitlab_rails['smtp_enable'] = true
        gitlab_rails['smtp_address'] = "smtp.sendgrid.net"
        gitlab_rails['smtp_port'] = 587
        gitlab_rails['smtp_user_name'] = 'apikey'
        gitlab_rails['smtp_password'] = '$SENDGRID_API_KEY_HERE'
        gitlab_rails['smtp_domain'] = "smtp.sendgrid.net"
        gitlab_rails['smtp_authentication'] = "login"
        gitlab_rails['smtp_enable_starttls_auto'] = true
        gitlab_rails['smtp_tls'] = false

        gitlab_rails['gitlab_default_theme'] = 2

        gitlab_rails['gitlab_shell_ssh_port'] = 2224

        gitlab_rails['gitlab_default_projects_features_container_registry'] = true
        gitlab_rails['registry_enabled'] = true
        gitlab_rails['registry_api_url'] = 'https://registry.example.com'
        gitlab_rails['registry_issuer'] = 'gitlab-issuer'
        registry['log_level'] = 'info'
        registry_external_url 'https://registry.example.com'
        registry_nginx['enable'] = true
        registry_nginx['listen_port'] = 5050
        registry_nginx['listen_https'] = false
        registry_nginx['redirect_http_to_https'] = false

        gitlab_shell['log_level'] = 'INFO'
        letsencrypt['enable'] = false
        nginx['error_log_level'] = 'info'
        nginx['listen_https'] = false
        #nginx['proxy_protocol'] = true
        #nginx['trusted_proxies'] = ["10.0.0.0/8", "172.16.0.0/12", "192.168.0.0/16"]

        # Workhorse
        gitlab_workhorse['enable'] = true
        gitlab_workhorse['ha'] = false
        gitlab_workhorse['listen_network'] = "tcp"
        gitlab_workhorse['listen_addr'] = "127.0.0.1:8181"
        gitlab_workhorse['log_directory'] = "/var/log/gitlab/gitlab-workhorse"

        # Errors
    # for sentry error logging the GitLab service
        #gitlab_rails['sentry_enabled'] = true
        #gitlab_rails['sentry_dsn'] = ''
        #gitlab_rails['sentry_clientside_dsn'] = ''
        #gitlab_rails['sentry_environment'] = 'production'
        # Add any other gitlab.rb configuration here, each on its own line
    networks:
      - nginx
    ports:
      # gitlab loves https on 443
      #- '80:80'
      #- '443:443'
      - '2224:22'
    volumes:
      - ./config:/etc/gitlab
      - ./logs:/var/log/gitlab
      - ./data:/var/opt/gitlab
    shm_size: '256m'
    #deploy:
    #  resources:
    #    limits:
    #      cpus: '6'
    #      memory: 12G
    #    reservations:
    #      cpus: '4'
    #      memory: 6G
    # disable healthcheck for restoring backup
    #healthcheck:
    #  disable: true
networks:
  nginx:
    external: true
    name: nginx