The only way you can unpublish a piece from your profile is to delete it, then re-enter it and while it’s still in “Edit status” submit to the publication of your choice. If there is another way, I am not privy to that, someone else might be.
Edited: Also, in order to get the three little dots, i.e., …, place the piece back in the “Edit” status, then the three little dots will appear to the right of the word, “Publish.” It will then drop down and you will be able to see the options to “Add to a publication” and other actions as well. Since you want to submit to a publication, you’ll choose, “Add to a publication,” a list of the publications you are affiliated with will come up. That will ensure that your piece is being submitted as a draft to the selected publication. Select the one you want and the rest is easy peasy. Also, this has to be done via desktop/or a more enhanced smart device other than a phone or via the mobile app.