Gitlab Pages : no pages:deploy after passed pages job

Question

I'm making a Java application. I want to generate and deploy the Javadoc after each commit on main. I'm using Maven to generate the files.

From the documentation:

When this pages job completes successfully, a special pages:deploy job appears in the pipeline view. It prepares the content of the website for the GitLab Pages daemon.

In the pipeline, the stage job runs successfully, but no stages:deploy in sight. There is no Deploy>Pages in the sidebar, and accessing group.domain.com/my_username/project-slug/pages is 404 (directly accessing a file supposed to be in public doesn't work either).
I also checked the job's artifact : the zip file just contains the public folder with the right files inside (including index.html).

Here is my .gitlab-ci.yml :

variables:
  MAVEN_OPTS: -Dmaven.repo.local=$CI_PROJECT_DIR/.m2/repository

default:
  image: maven:3.9.6-eclipse-temurin-21
  before_script:
    - mvn -version
    - cd winform-tester/

stages:
  - build
  - test
  - deploy
  - publish

cache:
  paths:
    - .m2/repository

build_job:
  stage: build
  script: 
    - mvn $MAVEN_OPTS compile

test_job:
  stage: test
  script: 
    - mvn $MAVEN_OPTS test
  artifacts:
    when: always
    paths:
      - winform-tester/target/surefire-reports/TEST-*.xml
    reports:
      junit:
        - winform-tester/target/surefire-reports/TEST-*.xml

pages:
  stage: publish
  script:
    - mvn $MAVEN_OPTS javadoc:javadoc
  after_script:
    - mv winform-tester/target/site/apidocs public
  artifacts:
    paths:
      - public
  only: 
    - main

Of course the jobs build_job and test_job are working as intended. Please tell me if you also need the pages job shell or pom.xml.

Thanks for the help.