How to run a job only once a MR gets merged and know what MR got merged?

Question

I'm trying to run a GitLab pipeline job to move a Trello card to a different list, when the corresponding MR gets merged, but the job needs the MR's IID, to fetch its description, which contains the card ID.

On a merge request pipeline, I can get the MR's IID from the CI_MERGE_REQUEST_IID env var, but merge request pipelines run when MRs are created/updated, not when they get merged.

This is the way I found to make the job run only when a MR gets merged:

move-card-to-done:
    stage: trello
    image: $MY_TRELLO_INTEGRATION_IMAGE
    tags:
        - docker
    only:
        - main
    when: on_success
    script:
        - moveCardToList $DONE_LIST_ID

The problem is that, since this is not a MR pipeline, the predefined variables I need are not available. By printing all available env vars, the only reference to the MR I found was in CI_COMMIT_MESSAGE, but since this is customizable, there's no guarantee about its content.

This seems like a legitimate use-case. Isn't there a reliable way to do this?