Keepeek - How do I move a media from a folder to another one ?

There is no direct way to do this action, you need to first add the media to the new folder, and then remove it from the old one. For that you need to use the medias representation of your folder.

Request to add the file to the new folder

POST /api/dam/folders/4567/medias
{
    "id": 12
}

Request to remove the file of the old folder

DELETE /api/dam/folders/1234/medias/12