delete gitlab-tag, create a new one, upload an artifact, create a new release and attach the artifact to it.

gitlab-retag-release.yml

upload_next:
  stage: deploy
  when: manual
  except:
    refs:
      - next
  only:
    - master
  needs: [ "package" ]
  dependencies: [ "package" ]
  image: registry.gitlab.com/gitlab-org/release-cli
  variables:
    GITLAB_URL: "$CI_SERVER_PROTOCOL://$CI_SERVER_HOST"
  script:
    - apk add curl zip jq
    - (cd compiled && zip -rq ../next-$CI_COMMIT_SHORT_SHA.zip .)
    - >
      export UPLOAD_RESPONSE=$(curl --request POST -s -H "PRIVATE-TOKEN: $GITLAB_API_TOKEN"
      --form "file=@next-$CI_COMMIT_SHORT_SHA.zip"
      "$GITLAB_URL/api/v4/projects/$CI_PROJECT_ID/uploads")
    - echo $UPLOAD_RESPONSE
    - export PACKAGE_PATH=$(echo "$UPLOAD_RESPONSE" | jq -r '.full_path')
    - >
      curl --request DELETE -H "PRIVATE-TOKEN: $GITLAB_API_TOKEN"
      "$GITLAB_URL/api/v4/projects/$CI_PROJECT_ID/repository/tags/next"
    - echo "$GITLAB_URL$PACKAGE_PATH"
    - >
      release-cli create --name next --description next --tag-name next --ref $CI_COMMIT_SHA
      --assets-link $(echo '{"name":"package","url":"'"$GITLAB_URL$PACKAGE_PATH"'","link_type":"package"}')

Because of https://gitlab.com/gitlab-org/gitlab/-/issues/24155 this is useless right now, but I wanted to persist it somewhere 😭
Once the API exists you could get the attached URL like this:

PROJECT_NAME=$(curl -s -H "PRIVATE-TOKEN: $GITLAB_API_TOKEN" $PROJECT_URL | jq -r '.name')
PACKAGE_LINK=$(curl -s -H "PRIVATE-TOKEN: $GITLAB_API_TOKEN" $PROJECT_URL/releases/next | jq -r '.assets.links[] | select (.name=="package") | .url')